Fundamentals of Math

Fundamentals of Mathematics

Chapter 7: Statistics Now that you understand how we can visualize data; it is time to learn how statisticians and data scientists like yourself delve more into the subject. Researchers are often interested in determining a value that best represents the data in the entire dataset. This helps them to summarize their findings. The value selected tends to be one that represents the centermost value in a dataset or the value that occurs most often. This value is known as a measure of central tendency. Measures of central tendency are summary statistics that represent the center point of a typical value of a dataset. The three most commonmeasures of central tendency are the mean, median, and mode. Each of these measures calculates the location of the central point using a different method. 7.1 Mean The mean is the average of the values in the data set. It is calculated by adding up the values of all the observations and then dividing the sum by the total number of observations.

∑

+ 2

+ 3

+ ⋯+

= 1

Mean =

The symbol Σ (sigma) is generally used to denote a sum of multiple terms. represents all the values in the dataset, and is the total number of observations in the dataset.

Example 7.1.1

9

7

6

4

6

8

9

Step 1: Add all the observations in the dataset together.

9 + 7 + 6 + 4 + 6 + 8 + 9 = 49

Step 2: Divide the sum from step 1 by the total number of observations in the dataset (7).

49 ÷ 7 = 7

The mean of this dataset is 7.

Practice 7.1

Directions: Find the mean of each of the following datasets.

1. 8, 9, 5, 8, 3, 7, 3, 9, 2

2. 6, 4, 3, 4, 5, 2

3. 3, 2, 3, 1, 8, 9, 8, 9, 8

4. 1, 5, 7, 3, 9, 6

Answer Key on Page 125

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