below are the batting averages for 50 baseball players. find the median, q1, and q3. median = q1 = q3 =

Explanation:

Step1: Sort the data

First, sort the 50 batting - averages in ascending order.

Step2: Find the median (Median)

Since (n = 50) (an even - numbered data set), the median is the average of the (\frac{n}{2}=25)th and (\left(\frac{n}{2}+1\right)=26)th ordered values. After sorting, the 25th value is (0.24) and the 26th value is (0.244). So, Median(=\frac{0.24 + 0.244}{2}=0.242).

Step3: Find the first quartile ((Q_1))

The first quartile is the median of the lower half of the data. The lower half consists of the first 25 values. Since (n = 25) (an odd - numbered data set), (Q_1) is the (\frac{25 + 1}{2}=13)th value in the sorted lower - half data. After sorting the lower half, (Q_1 = 0.214).

Step4: Find the third quartile ((Q_3))

The third quartile is the median of the upper half of the data. The upper half consists of the last 25 values. Since (n = 25) (an odd - numbered data set), (Q_3) is the (\frac{25+1}{2}=13)th value in the sorted upper - half data. After sorting the upper half, (Q_3 = 0.276).

Answer:

Median = (0.242) (Q_1=0.214) (Q_3 = 0.276)