Page 2 Math Study Guide for the CBEST

Statistical Principles

Operations

Statistical data can be described, summarized, presented, and interpreted using averages, range, minimum and maximum values, ratios, proportions, and percentile scores.

Mean, median, and mode are different ways of showing the average or central value of a set of data. Questions requiring to solve for the “average,” however, mostly refer to the “mean” unless otherwise stated. The mean of a set of data is computed by adding all the numbers in the set and dividing the resulting sum by how many numbers were added. The median is the middle number of a set of data sorted from the lowest to the highest. When there are two middle numbers, simply add them and divide by 2. The mode is the number that occurs the most number of times in the set. A set of data is said to be bimodal if it has two numbers occurring most often (equal number of times), and multimodal if there are more than two modes.

Probability

Probability measures the likelihood or the chance of an event occurring. To illustrate, imagine rolling a die. Let’s find out the probability of the die landing on the face with 5 dots.

A die has 6 faces. The possible outcomes when the die is thrown are: 1, 2, 3, 4, 5, and 6. Probability is computed as:

The probability that the die will land on the face with 5 dots is:

because there’s only 1 face with 5 dots, and there are 6 possible outcomes.

Test Score Interpretation

A student with a 70th percentile score means that he or she scored as good as or better than 70% of the class. Percentile is also called percentile rank, the value that shows the percentage of scores at or below the score in this rank.

Stanine score comes from “standard nine” referring to the nine units used in measuring students’ performance in a test. Tests scores are scaled from 1 to 9, with 5 as the mean. Students’ scores are ranked from lowest to highest. The lowest 4% belong to stanine 1; the next 7% belong to stanine 2; the next 12% stanine 3; the next 17% stanine 4; the next 20% stanine 5; the next 17% stanine 6; the next 12% stanine 7; the next 7% stanine 8; the last 4% stanine 9.