sara is practicing speed pole climbing. the data show her times in seconds. 16, 17.5, 17, 18, 16.5, 17…

sara is practicing speed pole climbing. the data show her times in seconds. 16, 17.5, 17, 18, 16.5, 17, 20\nwhat is the interquartile range (iqr) for saras data set?\nsaras iqr = seconds

sara is practicing speed pole climbing. the data show her times in seconds. 16, 17.5, 17, 18, 16.5, 17, 20\nwhat is the interquartile range (iqr) for saras data set?\nsaras iqr = seconds

Answer

Explanation:

Step1: Arrange data in ascending order

$16, 16.5, 16.5, 17, 17, 17.5, 18, 20$

Step2: Find the median (Q2)

Since there are 8 data - points, the median is the average of the 4th and 5th ordered values. So, $Q2=\frac{17 + 17}{2}=17$.

Step3: Find the lower half and Q1

The lower half of the data is $16, 16.5, 16.5, 17$. The median of the lower half (Q1) is the average of the 2nd and 3rd ordered values in the lower - half. So, $Q1=\frac{16.5+16.5}{2}=16.5$.

Step4: Find the upper half and Q3

The upper half of the data is $17, 17.5, 18, 20$. The median of the upper half (Q3) is the average of the 2nd and 3rd ordered values in the upper - half. So, $Q3=\frac{17.5 + 18}{2}=17.75$.

Step5: Calculate the IQR

$IQR=Q3 - Q1=17.75-16.5 = 1.25$

Answer:

$1.25$