match the values associated with this data set to their correct descriptions. (6, 47, 49, 15, 43, 41, 7, 36)…

Explanation:

Step1: Sort the data set

First, sort the data set ({6,47,49,15,43,41,7,36}) in ascending - order: ({6,7,15,36,41,43,47,49}).

Step2: Calculate the median

Since (n = 8) (an even - numbered data set), the median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+1))th values. (\frac{n}{2}=4) and (\frac{n}{2}+1 = 5). The 4th value is 36 and the 5th value is 41. Median(=\frac{36 + 41}{2}=38.5).

Step3: Calculate the first quartile

The lower half of the data set is ({6,7,15,36}). Since (n_1=4) (an even - numbered data set), the first quartile (Q_1) is the average of the (\frac{n_1}{2})th and ((\frac{n_1}{2}+1))th values. (\frac{n_1}{2}=2) and (\frac{n_1}{2}+1 = 3). The 2nd value is 7 and the 3rd value is 15. (Q_1=\frac{7 + 15}{2}=11).

Step4: Calculate the third quartile

The upper half of the data set is ({41,43,47,49}). Since (n_2 = 4) (an even - numbered data set), the third quartile (Q_3) is the average of the (\frac{n_2}{2})th and ((\frac{n_2}{2}+1))th values. (\frac{n_2}{2}=2) and (\frac{n_2}{2}+1 = 3). The 2nd value is 43 and the 3rd value is 47. (Q_3=\frac{43+47}{2}=45).

Step5: Calculate the difference of the largest value and the median

The largest value is 49 and the median is 38.5. The difference is (49−38.5 = 10.5).

Answer:

first quartile - 11 38.5 - median median - 38.5 11 - first quartile third quartile - 45 10.5 - the difference of the largest value and the median the difference of the largest value and the median - 10.5 45 - third quartile