251 Engineering Data Analysis and Probability Terms and Definitions | Mathematics Board Exam Review

INTRODUCTION

Engineering Data Analysis and Probability is one of the most directly applicable mathematics topics in the Philippine engineering licensure examinations. Every engineering discipline encounters data from material test results and quality control measurements to signal noise levels, failure rates, and environmental readings. The ability to collect, organize, describe, and draw conclusions from data using statistical and probabilistic tools is not just a board exam requirement. It is a core professional skill that working engineers use throughout their careers.

The PRC board examinations test this topic across all engineering programs. The mathematics section covers the theory: probability rules, discrete and continuous distributions, measures of central tendency and dispersion, sampling distributions, and basic inference. The major subject examinations embed these tools in engineering contexts such as reliability analysis, quality control, systems performance, and experimental design. Reviewees who understand both the vocabulary and the underlying logic of statistics and probability are far better equipped to handle both types of questions.

This glossary covers 251 terms drawn from the full scope of engineering data analysis and probability as covered in Mathematics engineering education and licensure review. The entries span descriptive statistics, probability theory, random variables, common probability distributions, sampling theory, estimation, hypothesis testing, regression and correlation, and applied statistical methods. Each definition is written to be precise, readable, and directly useful for board exam preparation. Terms are sorted alphabetically so you can use this as both a study guide and a quick reference.

The most important habit you can build while reviewing this topic is connecting each term to a calculation or a decision. Statistics is not just vocabulary and every term here has a formula, a condition, or a procedure attached to it. As you read through these definitions, ask yourself: What does this measure? When is it used? What does a large or small value of this quantity tell me about the data or the situation? That active reading approach is what converts a glossary review into genuine exam readiness.

The 251 Engineering Data Analysis and Probability Terms and Definitions

1. 68-95-99.7 Rule

See Empirical Rule. For normally distributed data, approximately 68%, 95%, and 99.7% of values lie within 1, 2, and 3 standard deviations of the mean, respectively.

2. Acceptance Region

The range of values of a test statistic for which the null hypothesis is not rejected in a hypothesis test. If the computed test statistic falls within the acceptance region, the data do not provide sufficient evidence to reject the null hypothesis at the chosen significance level.

3. Acceptance Sampling

A quality control procedure in which a random sample is taken from a batch of items and the batch is accepted or rejected based on the number of defects found in the sample. It uses binomial or hypergeometric probability models to design sampling plans with specified producer’s and consumer’s risk levels.

4. Accuracy

The degree to which a measured or computed value agrees with the true or accepted value. In statistics, accuracy refers to how close the expected value of an estimator is to the true parameter value. An accurate estimator has low bias. Accuracy is distinct from precision, which refers to consistency.

5. Addition Rule of Probability

The rule for computing the probability of the union of two events. For any two events A and B, P(A ∪ B) = P(A) + P(B) − P(A ∩ B). For mutually exclusive events, P(A ∩ B) = 0, so the rule simplifies to P(A ∪ B) = P(A) + P(B).

6. Alternative Hypothesis

The hypothesis that contradicts the null hypothesis and represents the claim that a researcher is trying to find evidence for. Denoted H₁ or Hₐ. The alternative hypothesis may be one-sided (greater than or less than) or two-sided (not equal to). Rejecting the null hypothesis is equivalent to accepting the alternative.

7. Analysis of Variance (ANOVA)

A statistical method used to test whether the means of three or more groups are equal by analyzing the sources of variation in the data. ANOVA partitions total variability into variation between groups and variation within groups and uses the F-distribution to assess significance. It is widely used in experimental design and quality engineering.

8. Arithmetic Mean

The sum of all values in a dataset divided by the number of values. The most commonly used measure of central tendency. For a dataset with values x₁, x₂, …, xₙ, the arithmetic mean is x̄ = (x₁ + x₂ + … + xₙ)/n. It is sensitive to extreme values (outliers).

9. Asymmetric Distribution

A probability distribution or frequency distribution that is not symmetric about its center. Asymmetric distributions are either positively skewed (tail extends to the right) or negatively skewed (tail extends to the left). Skewness is the numerical measure of asymmetry.

10. Average

A general term for any measure of central tendency, though most commonly used to refer to the arithmetic mean. In engineering contexts, average often refers to the mean value of a measured quantity over a sample or time period.

11. Average Deviation

See Mean Absolute Deviation. The average of the absolute values of all deviations from the mean.

12. Bar Chart

A graphical display of categorical or discrete data using rectangular bars whose heights or lengths are proportional to the frequency or relative frequency of each category. Bar charts are used to compare quantities across different categories.

13. Bayes’ Theorem

A formula for updating the probability of an event based on new evidence. For events A and B with P(B) > 0, Bayes’ theorem states P(A|B) = P(B|A) · P(A) / P(B). It allows prior probabilities to be revised into posterior probabilities when new data becomes available. It is fundamental to Bayesian statistics and reliability analysis.

14. Bell Curve

The characteristic symmetric, bell-shaped curve of the normal distribution. The peak of the bell curve occurs at the mean, and the curve extends symmetrically on both sides, decreasing toward zero as values move further from the mean. The bell curve is defined by its mean and standard deviation.

15. Bernoulli Distribution

The probability distribution of a random variable that takes the value 1 with probability p (success) and the value 0 with probability 1 − p (failure). It is the simplest discrete distribution and is the building block of the binomial distribution. Its mean is p and its variance is p(1 − p).

16. Bernoulli Trial

A single experiment or observation with exactly two possible outcomes, conventionally called success and failure, with fixed probabilities p and 1 − p respectively. The outcomes must be mutually exclusive and the trial must be independent of other trials. A sequence of Bernoulli trials forms the basis of the binomial distribution.

17. Beta Distribution

A continuous probability distribution defined on the interval [0, 1], commonly used to model proportions, probabilities, and completion rates in project management. It is parameterized by two shape parameters α and β and is flexible enough to represent a wide range of distributional shapes.

18. Bias

A systematic error that causes estimates to consistently deviate from the true value in one direction. An estimator is biased if its expected value does not equal the true parameter. Bias is different from random error and cannot be reduced by increasing sample size alone.

19. Bimodal Distribution

A probability or frequency distribution with two distinct peaks (modes). A bimodal distribution often indicates that the data come from two different subpopulations or processes. It is a form of multimodal distribution.

20. Binomial Coefficient

The number of ways to choose k items from n items without regard to order, denoted C(n, k) or (n choose k), computed as n! / (k!(n − k)!). Binomial coefficients appear as the probabilities in the binomial distribution and as the terms in the binomial theorem expansion.

21. Binomial Distribution

The discrete probability distribution of the number of successes in n independent Bernoulli trials, each with success probability p. The probability of exactly k successes is P(X = k) = C(n, k) · pᵏ · (1 − p)^(n − k). Its mean is np and its variance is np(1 − p). It is one of the most tested distributions in the board exam.

22. Binomial Experiment

An experiment consisting of a fixed number n of independent Bernoulli trials, each with the same probability of success p. A binomial experiment has exactly two outcomes per trial, a fixed number of trials, independent trials, and a constant probability of success. The count of successes follows a binomial distribution.

23. Binomial Probability Formula

The formula for computing the exact probability of k successes in n independent Bernoulli trials: P(X = k) = C(n, k) · pᵏ · (1 − p)^(n − k). This formula is one of the most frequently applied in the engineering board exam and must be committed to memory along with the values of the mean np and variance np(1 − p).

24. Bivariate Data

Data consisting of two variables measured on the same set of subjects or units. Bivariate data is used in correlation and regression analysis to study the relationship between the two variables. Scatter plots are the primary graphical tool for exploring bivariate data.

25. Bivariate Distribution

The joint probability distribution of two random variables X and Y considered together. It specifies the probability (for discrete variables) or probability density (for continuous variables) for all pairs of values (x, y). Marginal distributions of X and Y are derived from the bivariate distribution.

26. Box Plot

A graphical summary of a dataset showing the minimum, first quartile, median, third quartile, and maximum — the five-number summary. The box represents the interquartile range, the line inside the box is the median, and the whiskers extend to the minimum and maximum (or to 1.5 times the IQR for outlier detection).

27. Central Limit Theorem

One of the most important theorems in statistics, stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution, provided the population has a finite mean and variance. This theorem justifies the widespread use of normal-based inference methods.

28. Central Tendency

A statistical measure that identifies a single value as representative of an entire dataset by locating the center of the data distribution. The three main measures of central tendency are the mean, median, and mode. The choice of which measure to use depends on the type of data and the shape of its distribution.

29. Chebyshev’s Theorem

A theorem stating that for any distribution with finite mean μ and standard deviation σ, at least 1 − 1/k² of the data values lie within k standard deviations of the mean, for any k > 1. It applies to all distributions regardless of shape and provides a conservative lower bound on the proportion of data within a given range.

30. Chi-Square Distribution

A continuous probability distribution that arises when independent standard normal random variables are squared and summed. A chi-square random variable with ν degrees of freedom is the sum of ν squared standard normal variables. It is used in goodness-of-fit tests, tests of independence, and confidence intervals for variance.

31. Chi-Square Test

A hypothesis test using the chi-square distribution to assess whether observed frequencies differ significantly from expected frequencies (goodness-of-fit test) or whether two categorical variables are independent (test of independence). The test statistic is χ² = Σ (O − E)² / E, summed over all categories.

32. Class Boundary

The actual boundary value separating adjacent classes in a frequency distribution, computed as the average of the upper limit of one class and the lower limit of the next class. Class boundaries eliminate gaps between classes and are used to construct histograms.

33. Class Interval

The width of each class in a grouped frequency distribution, computed as the difference between the upper and lower class boundaries. All classes in a standard frequency distribution have equal class intervals, which simplifies computation and graphical representation.

34. Class Limit

The stated minimum (lower class limit) and maximum (upper class limit) values that can fall within a given class of a grouped frequency distribution. Class limits define the range of data values that belong to each class.

35. Class Mark

The midpoint of a class interval in a grouped frequency distribution, computed as the average of the upper and lower class limits. The class mark is used as a representative value for all data within that class when computing the mean, variance, and other statistics from grouped data.

36. Classical Probability

The probability model based on equally likely outcomes. If a sample space has N equally likely outcomes and an event A contains n of them, then P(A) = n/N. Classical probability applies to games of chance and situations with symmetry. Also called theoretical probability or a priori probability.

37. Coefficient of Correlation

See Pearson Correlation Coefficient. A dimensionless measure of the strength and direction of the linear relationship between two quantitative variables, ranging from −1 to +1.

38. Coefficient of Determination

The square of the correlation coefficient, denoted r², representing the proportion of the total variation in the dependent variable that is explained by the regression model. An r² value of 0.85 means 85% of the variation in y is accounted for by the linear relationship with x.

39. Coefficient of Variation

The ratio of the standard deviation to the mean, expressed as a percentage: CV = (σ/μ) × 100%. It is a dimensionless measure of relative variability that allows comparison of variability between datasets with different units or different means. A higher CV indicates greater relative variability.

40. Collectively Exhaustive Events

A set of events is collectively exhaustive if their union covers the entire sample space, meaning every possible outcome is included in at least one of the events. Together with mutual exclusivity, collective exhaustiveness defines a partition of the sample space.

41. Combination

The number of ways to select k items from n distinct items without regard to order, denoted C(n, k) = n! / (k!(n − k)!). Combinations differ from permutations in that order does not matter. Combinations are used in computing binomial probabilities and in counting problems on the board exam.

42. Complement of an Event

The set of all outcomes in the sample space that are not in the event A, denoted A’ or Aᶜ. The probability of the complement satisfies P(A’) = 1 − P(A). Using the complement rule often simplifies probability calculations for events involving “at least one” or “none.”

43. Complement Rule

The rule stating that P(A’) = 1 − P(A) for any event A in a sample space. If the probability of an event is known, the probability of its complement is immediately determined. This rule is especially useful when it is easier to compute the probability of the complement than the event itself.

44. Complementary Counting

A counting strategy that determines the number of ways an event can occur by subtracting the number of unfavorable outcomes from the total. It mirrors the complement rule in probability and is especially useful when the complementary count is simpler than the direct count.

45. Conditional Distribution

The probability distribution of a random variable given that another random variable takes a specific value. For discrete variables, P(X = x | Y = y) = P(X = x, Y = y) / P(Y = y). Conditional distributions describe how the distribution of one variable changes when the other variable is fixed.

46. Conditional Probability

The probability of event A occurring given that event B has already occurred, defined as P(A|B) = P(A ∩ B) / P(B), provided P(B) > 0. Conditional probability accounts for information provided by the occurrence of B and is fundamental to Bayes’ theorem, independence testing, and reliability analysis.

47. Confidence Interval

A range of values computed from sample data that is expected to contain the true population parameter with a specified probability (confidence level). A 95% confidence interval means that if the procedure were repeated many times, 95% of the resulting intervals would contain the true parameter.

48. Confidence Interval for the Mean

An interval of the form x̄ ± z*(σ/√n) (for known σ) or x̄ ± t*(s/√n) (for unknown σ) that estimates the population mean μ with a specified level of confidence. The width of the interval decreases as sample size increases or confidence level decreases.

49. Confidence Level

The probability (expressed as a percentage) that a confidence interval constructed from a random sample contains the true population parameter. Common confidence levels are 90%, 95%, and 99%. Higher confidence levels produce wider intervals.

50. Contingency Table

A two-way table displaying the joint frequency distribution of two categorical variables. Each cell contains the count of observations falling into the corresponding combination of categories. Contingency tables are used in chi-square tests of independence.

51. Continuous Data

Data arising from measurements that can take any value within a range, such as temperature, pressure, length, and time. Continuous data are described by probability density functions and are analyzed using the full set of parametric statistical methods.

52. Continuous Random Variable

A random variable that can take any value within a continuous interval or range. The probability of a continuous random variable taking any specific value is zero. Probabilities are computed over intervals using the probability density function. Examples include height, weight, temperature, and time.

53. Continuous Uniform Distribution

A continuous distribution in which all values in an interval [a, b] are equally likely. The probability density function is f(x) = 1/(b − a) for a ≤ x ≤ b. Its mean is (a + b)/2 and its variance is (b − a)²/12. It models complete uncertainty over a bounded interval.

54. Control Chart

A time-series graph used in statistical process control to monitor whether a process is operating within its expected variation. It displays measurements over time along with control limits set at ±3 standard deviations from the process mean. Points outside the control limits signal a potentially out-of-control process.

55. Correlation

A statistical measure of the strength and direction of the linear relationship between two quantitative variables. Correlation values range from −1 (perfect negative linear relationship) to +1 (perfect positive linear relationship), with 0 indicating no linear relationship. Correlation does not imply causation.

56. Correlation vs. Causation

The fundamental principle that a statistical correlation between two variables does not necessarily imply that one causes the other. Both variables may be caused by a third confounding variable, or the correlation may be coincidental. Establishing causation requires controlled experiments, not just observed data.

57. Correlation Coefficient

A numerical value measuring the strength and direction of the linear association between two variables. The Pearson correlation coefficient r is the most widely used form. It is computed as the ratio of the covariance of X and Y to the product of their standard deviations.

58. Counting Principle

See Fundamental Counting Principle. The rule that if one event can occur in m ways and a second independent event can occur in n ways, then both events together can occur in m × n ways.

59. Counting with Repetition

Counting arrangements or selections where items may be repeated. The number of ordered arrangements of r items chosen from n distinct items with repetition is nʳ. This contrasts with permutations without repetition where each item can be chosen only once.

60. Covariance

A measure of the joint variability of two random variables X and Y, defined as the expected value of the product of their deviations from their respective means: Cov(X, Y) = E[(X − μₓ)(Y − μᵧ)]. Positive covariance indicates that the variables tend to move in the same direction. Covariance is the unnormalized version of correlation.

61. Critical Region

The set of values of a test statistic for which the null hypothesis is rejected. Also called the rejection region. If the computed test statistic falls in the critical region, the result is statistically significant at the chosen significance level. The critical region is determined by the significance level and the direction of the test.

62. Critical Value

The boundary value separating the acceptance region from the rejection region in a hypothesis test. It is determined by the significance level and the distribution of the test statistic. Common critical values from the standard normal distribution are ±1.645 for a 10% two-tailed test and ±1.96 for a 5% two-tailed test.

63. Cumulative Distribution Function

A function F(x) = P(X ≤ x) that gives the probability that a random variable X takes a value less than or equal to x. The CDF is defined for both discrete and continuous random variables, is non-decreasing, approaches 0 as x → −∞, and approaches 1 as x → +∞.

64. Cumulative Frequency

The running total of frequencies up to and including a particular class or value in a frequency distribution. Cumulative frequencies are used to construct ogives and to determine percentiles and quartiles from grouped data.

65. Cumulative Poisson Probabilities

The probability that a Poisson random variable X is less than or equal to a given value, P(X ≤ k) = Σᵢ₌₀ᵏ e^(−λ)λⁱ/i!. Cumulative Poisson probabilities are read from Poisson tables provided in exam materials or computed directly from the formula.

66. Cumulative Relative Frequency

The running total of relative frequencies up to and including a particular class, expressed as a proportion or percentage of the total. It equals the cumulative frequency divided by the total number of observations and ranges from 0 to 1 (or 0% to 100%).

67. Data

Recorded observations or measurements collected for analysis. In engineering and statistics, data can be qualitative (categorical) or quantitative (numerical). Quantitative data can be further classified as discrete (countable values) or continuous (measurable values on a continuous scale).

68. Data Collection

The process of gathering observations or measurements from a population or process. Methods include surveys, experiments, observational studies, and automated sensor readings. The quality and method of data collection determine the validity of all subsequent analyses and conclusions.

69. Data Set

A collection of related data values or observations, typically organized in a structured format such as a table, list, or database. A data set may consist of a single variable (univariate) or multiple variables (multivariate).

70. Decile

Any of the nine values that divide a sorted dataset into ten equal parts. The first decile D₁ is the value below which 10% of the data fall, the second decile D₂ is the value below which 20% fall, and so on. Deciles are a type of quantile used for detailed distributional analysis.

71. Degrees of Freedom

The number of independent pieces of information available to estimate a statistical parameter. For a sample variance computed from n observations, the degrees of freedom is n − 1 because one degree of freedom is used to estimate the mean. Degrees of freedom determine the specific shape of t, chi-square, and F distributions.

72. Degrees of Freedom in Chi-Square Tests

For goodness-of-fit tests, degrees of freedom equals the number of categories minus 1 minus the number of estimated parameters. For tests of independence in an r × c contingency table, degrees of freedom equals (r − 1)(c − 1). The degrees of freedom determine which chi-square distribution is used.

73. Dependent Events

Two events A and B are dependent if the occurrence of one affects the probability of the other. Formally, A and B are dependent if P(A|B) ≠ P(A) or equivalently P(A ∩ B) ≠ P(A) · P(B). Most real-world events involving sampling without replacement are dependent.

74. Descriptive Statistics

The branch of statistics concerned with organizing, summarizing, and presenting data in a meaningful way. Descriptive statistics include measures of central tendency (mean, median, mode), measures of variability (range, variance, standard deviation), graphical displays, and frequency distributions. They describe the sample without drawing inferences about the population.

75. Deviation

The difference between an individual data value and a reference value, most commonly the mean. Deviations measure how far each observation is from the center of the distribution. The sum of all deviations from the mean is always zero.

76. Discrete Data

Data consisting of counts or values that can take only specific separate values, typically integers. Examples include the number of defective items, the number of customers per hour, and the number of accidents per month. Discrete data are described by probability mass functions.

77. Discrete Random Variable

A random variable that can take only a countable number of distinct values, often integers. Each value has a specific probability assigned to it, and the sum of all probabilities equals 1. Examples include the number of defective items in a batch, the number of accidents per day, and the number of successes in a fixed number of trials.

78. Discrete Uniform Distribution

A discrete distribution in which each of n equally likely values has probability 1/n. Rolling a fair die is an example. The mean is (n + 1)/2 and the variance is (n² − 1)/12 for values 1, 2, …, n.

79. Disjoint Events

See Mutually Exclusive Events. Two events that cannot occur simultaneously, having no outcomes in common.

80. Distribution

A description of how the values of a random variable or dataset are spread across possible outcomes. A distribution can be described by a probability mass function (discrete), probability density function (continuous), or a frequency table (empirical). The shape, center, and spread of a distribution are its key features.

81. Empirical Probability

Probability estimated from observed data rather than theoretical reasoning. Also called relative frequency probability or a posteriori probability. If an event occurs f times in n trials, its empirical probability is estimated as f/n. As n increases, empirical probability converges to the theoretical probability by the Law of Large Numbers.

82. Empirical Rule

The rule stating that for a normally distributed dataset, approximately 68% of values lie within 1 standard deviation of the mean, approximately 95% lie within 2 standard deviations, and approximately 99.7% lie within 3 standard deviations. Also called the 68-95-99.7 rule.

83. Error

The difference between an observed value and the true or expected value. In statistics, error can be due to random variation (random error) or systematic causes (bias). In hypothesis testing, Type I error is rejecting a true null hypothesis and Type II error is failing to reject a false null hypothesis.

84. Error Bars

Graphical representations of the variability in plotted data, shown as lines extending above and below data points in a graph. Error bars may represent standard deviation, standard error, or confidence interval width. They communicate the precision or reliability of measurements.

85. Error Sum of Squares

In regression and ANOVA, the sum of the squared differences between observed values and fitted (predicted) values. It measures the unexplained variation in the dependent variable after accounting for the regression model. Minimizing the error sum of squares is the criterion used in the method of least squares.

86. Estimation

The process of using sample data to infer the value of an unknown population parameter. Estimation can produce a point estimate (a single value) or an interval estimate (a range of values). Good estimators are unbiased, consistent, and efficient.

87. Event

A subset of the sample space in a probability experiment. An event may consist of one outcome (simple event) or multiple outcomes (compound event). The probability of an event is the sum of the probabilities of its constituent outcomes.

88. Event Space

The set of all possible events that can be defined on a given sample space, including the sample space itself and the empty set. The event space is closed under union, intersection, and complementation, forming the mathematical structure (sigma-algebra) on which probabilities are defined.

89. Expected Value

The long-run average value of a random variable, computed as the weighted sum of all possible values using their probabilities as weights. For a discrete random variable, E(X) = Σ x · P(X = x). The expected value is the mean of the probability distribution and represents the center of the distribution.

90. Experiment

In probability, any process or procedure that generates observations or outcomes that are subject to uncertainty. The set of all possible outcomes of an experiment is the sample space. A single performance of the experiment produces one outcome from the sample space.

91. Experimental Design

The planning and structuring of experiments to collect data efficiently and draw valid statistical conclusions. Key principles include randomization (to control bias), replication (to estimate variability), and blocking (to reduce the effect of nuisance variables). Good experimental design is essential for reliable inference.

92. Exponential Distribution

A continuous probability distribution describing the time between events in a Poisson process. Its probability density function is f(x) = λe^(−λx) for x ≥ 0, where λ is the rate parameter. Its mean is 1/λ and its variance is 1/λ². The exponential distribution has the memoryless property and is widely used in reliability and queuing analysis.

93. Extrapolation

The use of a regression model to predict values of the dependent variable for values of the independent variable outside the range of the observed data. Extrapolation is unreliable because the linear (or other) relationship may not hold beyond the data range. Board exam problems sometimes test awareness of this limitation.

94. F-Distribution

A continuous probability distribution that arises as the ratio of two independent chi-square random variables, each divided by its degrees of freedom. It is used in ANOVA and in tests comparing two population variances. The F-distribution is right-skewed and depends on two degrees of freedom parameters.

95. F-Test

A hypothesis test using the F-distribution to compare two population variances or to test overall significance in ANOVA. The test statistic is the ratio of two sample variances or mean squares. A large F-statistic suggests the variances (or group means) are significantly different.

96. Factorial

The product of all positive integers from 1 to n, denoted n! = n × (n − 1) × (n − 2) × … × 1. By convention, 0! = 1. Factorials appear in permutation and combination formulas and in the probability mass functions of the binomial and Poisson distributions.

97. Failure Rate

In reliability engineering, the rate at which a component or system fails per unit time. For the exponential distribution, the failure rate is the constant parameter λ. The failure rate is the reciprocal of the mean time between failures (MTBF) and is a key metric in reliability analysis.

98. Favorable Outcome

An outcome in a probability experiment that belongs to the event of interest. In classical probability, P(A) = (number of favorable outcomes) / (total number of equally likely outcomes). The concept of favorable outcomes is fundamental to elementary probability calculations.

99. Five-Number Summary

A concise description of a dataset consisting of the minimum value, first quartile Q1, median Q2, third quartile Q3, and maximum value. The five-number summary provides a complete picture of the center, spread, and extremes of the distribution and is the basis for the box plot.

100. Frequency

The number of times a particular value or class of values occurs in a dataset. Frequency counts form the basis of frequency distributions, histograms, and most descriptive statistical analyses. Relative frequency expresses frequency as a proportion of the total count.

251. z-Test

A hypothesis test based on the standard normal distribution used when the population standard deviation σ is known or when the sample size is large (n ≥ 30). The test statistic is z = (x̄ − μ₀)/(σ/√n) for testing claims about a population mean.

Conclusion

For the Mathematics engineering board exam, the highest-priority areas in this topic are probability rules (addition, multiplication, complement, and conditional probability), the binomial and Poisson distributions, the normal distribution and z-score calculations, and the basic measures of descriptive statistics: mean, median, mode, variance, and standard deviation. These are the concepts that appear most frequently and most consistently across years and disciplines. Every reviewee, regardless of their engineering program, should have these computations completely automated before sitting the exam.

After the fundamentals, focus on the connections between concepts. The Central Limit Theorem connects sampling distributions to the normal distribution. Confidence intervals connect point estimation to probability. The chi-square, t, and F distributions each extend the normal distribution to solve specific inference problems. Regression and correlation are connected through the coefficient of determination. Understanding these connections rather than memorizing isolated formulas allows you to work through unfamiliar problems by reasoning from first principles, which is exactly what the more challenging board exam items require.

Finally, pay careful attention to conditions and assumptions. Many statistical tests require normality, independence, or minimum sample sizes to be valid. Board exam problems sometimes test whether you know when a method can and cannot be applied and not just how to apply it. The binomial approximation to the normal requires np ≥ 5 and n(1−p) ≥ 5. The t-test is used when σ is unknown and the sample is small. The chi-square test requires expected frequencies of at least 5 per cell. Knowing these conditions and being able to identify the correct method for a given situation is the difference between a reviewer who can solve textbook exercises and one who can pass the actual licensure examination.

For practice problems on all these topics, head over to our Venn Diagram Problems, Combination Problems, Permutation Problems, Probability Problems and Solutions section here on PinoyBix. Hundreds of solved exam-type questions, complete with step-by-step solutions, organized by topic so you can drill exactly what you need to work on.