The data to represent average test scores for a class of 16 students includes an outlier value of 78. if the outlier is included, then the mean is 84. which statement is always true about the new data when the outlier is removed? a. the mean would decrease. b. the mean would increase. c. the median would decrease. d. the median would increase.
Option C (The mean would decrease).
In this question, there are 16 observations and their mean is 80. There is an outlier which has the value 91. This means that the outlier is on the greater side of the mean. The formula for mean is:
Mean = Sum of observations/Number of Observations.
Sum of observations can be calculated by substituting the values in the above formula.
80 = Sum/16.
Sum = 80*16 = 1280.
Subtracting 91 from the total sum will give the sum of rest of the 15 non-outlier values. Therefore 1280 - 91 = 1189.
Calculating the mean of the 15 values:
Mean = 1189/15 = 79.267 (correct to 3 decimal places).
It can be seen that removing the outlier decreases the mean. Therefore C is the correct answer. The information regarding the median cannot be determined since actual values are not present, which are required to calculate the median. Therefore, C is the correct choice!!!
When the outlier is removed The mean would increase.
Outliers are the value that lies outside the set of data. i.e. the data doesn't fit in the group.
Removing outliers can affect mean more than median. Because outlier removal sometimes affect the median but in a small percentage or sometimes it will remain the same.
Let us prove, consider 16 values one with 78 and other 15 with values nearly 85, 84 that will give the mean value as 84.
78, 84, 82, 86, 84, 85, 83, 86, 82, 85, 84, 83, 86, 85, 86, 85.
Mean = 84.
Remove 78 from the data set then the data set is 84, 82, 86, 84, 85, 83, 86, 82, 85, 84, 83, 86, 85, 86, 85 and number of data is reduced to 15.
Mean = 84.4.
The mean is increased.
3) The median for Week 2 is more than the median for Week 1.
4) The interval of 0-19 will increase by 20 of either Hay Bale Toss or Pie Eating Contest.
5) There is a significant outlier at the low end for the females.
6) the mean decreases by 2.75.
7) The 4th period class should get the reward.
8) The answer is C, if the outlier were included in the data, the median would not significantly change.
10) There is one outlier that indicates an unusually large number of players on that team.