Question

1. the data represent the number of cans collected by different classes for a service project. (lesson 1 - 9) 12 14 22 14 18 23 42 13 9 19 22 14 a. find the mean. b. find the median. c. eliminate the greatest value, 42, from the data set. explain how the measures of center change.

Explanation:

Step1: Calculate sum of data

$12 + 14+22 + 14+18+23+42+13+9+19+22+14=222$

Step2: Find number of data points

There are 12 data - points.

Step3: Calculate the mean

Mean = $\frac{222}{12}=18.5$

Step4: Arrange data in ascending order

$9, 12, 13, 14, 14, 14, 18, 19, 22, 22, 23, 42$

Step5: Calculate the median

Since there are 12 data - points, the median is the average of the 6th and 7th ordered values. Median=$\frac{14 + 18}{2}=16$

Step6: Remove 42 from the data set

New data set: $9, 12, 13, 14, 14, 14, 18, 19, 22, 22, 23$

Step7: Calculate new sum

$9+12+13+14+14+14+18+19+22+22+23 = 170$

Step8: Calculate new mean

There are 11 data - points. New mean=$\frac{170}{11}\approx15.45$

Step9: Calculate new median

Since there are 11 data - points, the median is the 6th ordered value, which is 14.

Step10: Analyze change in measures of center

The mean decreased from 18.5 to approximately 15.45 because the large value (42) was removed, pulling the mean down. The median decreased from 16 to 14. The removal of the out - lier 42 affected the mean more than the median as the mean is sensitive to extreme values while the median is a positional measure.

Answer:

a. 18.5
b. 16
c. The mean decreased from 18.5 to approximately 15.45 and the median decreased from 16 to 14. The mean is more affected by the removal of the outlier 42 as it is sensitive to extreme values while the median is a positional measure.