Exercise 6 Page 791

We are given the following data set. 39, 52, 41, 44, 47, 36, 51, 44, 50, 40, 53, 46, 44, 35 The first thing that should be done when finding the key features of a data set is rearranging the numbers from least to greatest. 35, 36, 39, 40, 41, 44, 44, 44, 46, 47, 50, 51, 52, 53Let's proceed to finding the mean, median, mode and range.

Mean

The mean of a data set is calculated by finding the sum of all values in the set and then dividing by the number of values in the set. In this case, there are 14 values in the set.

Median

To identify the median, we observe the middle value. 35, 36, 39, 40, 41, 44, 44 | 44, 46, 47, 50, 51, 52, 53 There is no middle value. When this happens, we need to calculate the median by finding the average of the two values closest to the middle. When arranged from least to greatest, 44 and 44 are the most central values. Median: 44+ 44/2=44

Mode

The mode of a data set is the value that occurs most frequently. 35, 36, 39, 40, 41, 44, 44, 44, 46, 47, 50, 51, 52, 53 We can see that 44 occurs more frequently than any other value in the set, so this is the mode.

Range

The range is the difference between the greatest and the least data values. 35, 36, 39, 40, 41, 44, 44, 44, 46, 47, 50, 51, 52, 53 We can see that 35 is the least value and 53 is the greatest value in the data set. Now we can calculate the data range. Range: 53- 35=18

Which Measure Is Best?

Since there are no outliers, the best measure is the mean. In this case, the difference between the mean 44.4, the median 44, and the mode 44 is not that large. Therefore the last two are also good measures for the data.