Question

find the range and interquartile range (iqr) of the following data set. 70, 65, 75, 85, 90. press each hotspot. label the corresponding number below with the requested value. press to hear a reminder or hint for this problem. the range is the difference between the greatest and least

Explanation:

Step1: Find the range

Range = Max - Min. The maximum value in the data - set {70, 65, 75, 85, 90} is 90 and the minimum value is 65. So, Range = 90 - 65.
$90 - 65=25$

Step2: Find the median

First, order the data - set: 65, 70, 75, 85, 90. Since there are 5 values (an odd number), the median is the middle value, which is 75.

Step3: Find the lower and upper quartiles

The lower half of the data - set is {65, 70}, and its median (lower quartile $Q_1$) is $\frac{65 + 70}{2}=67.5$. The upper half of the data - set is {85, 90}, and its median (upper quartile $Q_3$) is $\frac{85+90}{2}=87.5$.

Step4: Calculate the inter - quartile range (IQR)

IQR = $Q_3−Q_1$. So, IQR = 87.5 - 67.5.
$87.5 - 67.5 = 20$

Answer:

Range: 25; IQR: 20