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

Sort ${6, 47, 49, 15, 43, 41, 7, 36}$ in ascending - order: ${6, 7, 15, 36, 41, 43, 47, 49}$.

Step2: Calculate the median

Since there are $n = 8$ data points, the median is the average of the $\frac{n}{2}$ - th and $(\frac{n}{2}+1)$ - th ordered values. $\frac{36 + 41}{2}=38.5$.

Step3: Calculate the first - quartile

The lower half of the data set is ${6, 7, 15, 36}$. Since there are $n_1 = 4$ data points in the lower half, the first - quartile is the average of the $\frac{n_1}{2}$ - th and $(\frac{n_1}{2}+1)$ - th ordered values in the lower half. $\frac{7 + 15}{2}=11$.

Step4: Calculate the third - quartile

The upper half of the data set is ${41, 43, 47, 49}$. Since there are $n_2 = 4$ data points in the upper half, the third - quartile is the average of the $\frac{n_2}{2}$ - th and $(\frac{n_2}{2}+1)$ - th ordered values in the upper half. $\frac{43+47}{2}=45$.

Step5: Calculate the difference between 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 $\leftrightarrow$ 11 median $\leftrightarrow$ 38.5 third quartile $\leftrightarrow$ 45 the difference of the largest value and the median $\leftrightarrow$ 10.5