Question

Ms Almquist wants to know how long it takes students to read a chapter. She timed how long it took kids to read a chapter during class. The data points are shown below in mins. 12,15,14,10,42,16,13 Which measure of center would be most affected by the outlier of 42 min? Is it A median B mode C mean D range I will give you 100 points plz

Answer 1

range ⇒ answer D

Explanation:

* Lets explain how to solve the problem

- Outlier an extreme value in a set of data which is much higher or

lower than the other numbers

- Outliers affect the mean value of the data but have little effect on the

median or mode of a given set of data

* Lets solve the problem

∵ The data are 10 , 12 , 13 , 14 , 15 , 16 , 42

∵ The median is the middle number of the set of data

∵ The middle number is 14

∴ The median is 14

- If we remove the outlier then:

∴ The median will be the average of the two middle numbers 13 , 14

∴ The median = (13 + 14)/2 = 13.5

∵ The mean is the average, where you add all the numbers and then

divide the sum by the number of numbers

∵ The sum = 10 + 12 + 13 + 14 + 15 + 16 + 42 = 122

∵ They are 7 numbers

∴ The mean = 122/7 = 17.43

- If we remove the outlier then:

∴ The sum = 122 - 42 = 80

∴ The mean = 80/7 = 11.43

∵ The range is the difference between the greatest and the

smallest values of the data set

∵ The greatest value is 42 and the smallest value is 10

∴ The range = 42 - 10 = 32

- If we remove the outlier then:

∴ The range = 16 - 10 = 6

* The range is the most affected by the outlier