Question

the sixth grade is holding a canned - food drive. the number of cans collected each day was 45, 21, 3, 15, 32, 97, 68, 27, 29, and 52. what is the interquartile range of cans collected each day? find the lower - quartile, upper - quartile, and interquartile range: lower quartile = cans upper quartile = cans interquartile range = cans 21 31 32 52

Explanation:

Step1: Arrange data in ascending order

3, 15, 21, 27, 29, 32, 45, 52, 68, 97

Step2: Find the median

There are 10 data - points. The median is the average of the 5th and 6th ordered values. Median $=\frac{29 + 32}{2}=30.5$

Step3: Find the lower - half and upper - half of data

The lower - half is 3, 15, 21, 27, 29. The upper - half is 32, 45, 52, 68, 97.

Step4: Find the lower - quartile ($Q_1$)

The lower - quartile is the median of the lower - half. Since there are 5 values in the lower - half, the lower - quartile is the 3rd value. So, $Q_1 = 21$

Step5: Find the upper - quartile ($Q_3$)

The upper - quartile is the median of the upper - half. Since there are 5 values in the upper - half, the upper - quartile is the 3rd value. So, $Q_3 = 52$

Step6: Calculate the inter - quartile range (IQR)

$IQR=Q_3 - Q_1=52 - 21 = 31$

Answer:

Lower quartile = 21 cans
Upper quartile = 52 cans
Interquartile range = 31 cans