When the outliers are removed how does the mean change?
1 dot on 50
2 dots on 72
1 dot on 74
1 dot on 76
1 dot on 78
3 dots in between 78 and 80
1 dot on 80
1 dot between 80 and 82
3 dots on 82
the mean decreases by 1.9
the mean decreases by 2.4
the mean decreases by 1.9
there are no outliers

The mean increases by 2.1

Step-by-step explanation:

According to the given description (dots are denoting the frequency for each value), the given data is :-

50 , 72, 72 , 74, 76 , 78 , 79 , 79 , 79 80, 81, 82, 82, 82

[Note - We take 79 as the value between 78 and 80, 81 as between 80 and 82 ]

Mean =                   (1)

First Quartile: Median of the lower half ( 50 , 72, 72 , 74, 76 , 78 , 79 )

= 74

Third Quartile: Median of the upper half (  79 , 79 80, 81, 82, 82, 82 )

= 81

Interquartile range (IQR)=

According to the IQR rule,

Upper limit =

Lower limit =

Since 50 < 63.2 , so 50 is outlier .

When 50 is removed from the data , the new data will be 72, 72 , 74, 76 , 78 , 79 , 79 , 79 80, 81, 82, 82, 82

Mean =

     (2)

Change in mean from (1) and (2)

Hence,  the mean increases by 2.1.

step-by-step explanation: