the data set below represents the total number of home runs that a baseball player hit each season for 11…

the data set below represents the total number of home runs that a baseball player hit each season for 11 seasons of play. what is the interquartile range of the data? 14, 22, 19, 21, 30, 32, 25, 15, 16, 27, 28\no 12\no 16\no 22\no 28

Answer

Explanation:

Step1: Arrange data in ascending order

$14, 15, 16, 19, 21, 22, 25, 27, 28, 30, 32$

Step2: Find the median (Q2)

Since there are 11 data - points, the median is the 6th value. So, $Q2 = 22$.

Step3: Find the lower half of data

The lower half is $14, 15, 16, 19, 21$. The median of the lower half (Q1) is the 3rd value, so $Q1 = 16$.

Step4: Find the upper half of data

The upper half is $25, 27, 28, 30, 32$. The median of the upper half (Q3) is the 3rd value of this half, so $Q3 = 28$.

Step5: Calculate the inter - quartile range (IQR)

$IQR=Q3 - Q1$. Substitute $Q1 = 16$ and $Q3 = 28$ into the formula: $IQR=28 - 16=12$.