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# Averages, Probability, and Combinations for CBEST Exam Study Guide (page 2)

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Updated on Mar 29, 2011

### Frequency Charts

Some average problems on the CBEST use frequency charts.

#### Sample Frequency Chart Question

1. The following list shows class scores for a Science 101 quiz. What is the average of the scores?
1. 28.5
2. 85
3. 91
4. 95
5. 100

Use the four Success Steps to solve the problem.

1. In this frequency chart, the test score is given on the right, and the number of students who received each grade is on the left: 10 students got a 100, 15 got a 90, etc.
2. Multiply the number of students by the score, because to find the average, each student's grade has to be added individually:
10 × 100 = 1,000
15 × 90 = 1,350
3 × 80 = 240
2 × 70 = 140
3. Then add the multiplied scores:
1,000 + 1,350 + 240 + 140 = 2,730
4. Divide the total number of students, 30 (10 + 15 + 3 + 2), into 2,730 to get the average: = 91.

### Other Average Problems

There are other kinds of averages besides the mean, which is usually what is meant when the word average is used:

• Median is the middle number in a data set after the set is ordered.
• Mode is the number that occurs most frequently.
• Range is the difference between the highest and lowest number.

#### Sample Median Question

1. What is the median of 6, 8, 3, 9, 4, 3, and 12?
1. 2
2. 6
3. 9
4. 10
5. 12

To get a median, put the numbers in order—3, 3, 4, 6, 8, 9, 12—and choose the middle number: 6. If there are an even number of numbers, average the middle two (you probably won't have to do that on the CBEST).

#### Four Success Steps for Probability Questions

1. Make a fraction.
2. Place the total number of different possibilities on the bottom.
3. Place the number of possibilities that make an event true on the top.
4. If the answers are in a:b form, place the numerator of the fraction first, and the denominator second.

#### Mode

The mode is the number used most frequently in a series of numbers. In the sample median question, the mode is 3 because 3 appears twice and all other numbers are used only once. Look again at the frequency table from the frequency chart sample question. Can you find the mode? More students (15) earned a score of 90 than any other score. Therefore, the mode is 90.

#### Range

To obtain the range, subtract the smallest number from the largest number. The range in the median sample question is 12 – 3, or 9. The range in the frequency chart sample question is 100 – 70, or 30.

### Probability

Suppose you put one entry into a drawing that had 700 entrants. What would be your chances of winning? They would be 1 in 700 of course. Suppose you put in two entries. Your chances would then be 2 in 700, or reduced, 1 in 350. Probabilities are fairly simple if you remember the few tricks that are explained in this section.