Question

When the outliers are removed how does the mean change?

Answer 1

Answer: 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 = $\overline{x}_1=\dfrac{\text{Sum of observations}}{\text{No. of observations}}$                   (1)

$=\dfrac{1066}{14}=76.1428571429\approx76.1$

First Quartile: $Q_1=$ Median of the lower half ( 50 , 72, 72 , 74, 76 , 78 , 79 )

= 74

Third Quartile: $Q_3=$ Median of the upper half (  79 , 79 80, 81, 82, 82, 82 )

= 81

Interquartile range (IQR)=$Q_3-Q_1=81-74=7$

According to the IQR rule,

Upper limit = $1.5\times IQR+Q_3=1.5\times7+81=91.5$

Lower limit = $Q_1-1.5\times IQR=74-1.5\times7=63.5$

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 = $\overline{x}_2=\dfrac{\text{Sum of observations}}{\text{No. of observations}}$

$=\dfrac{1016}{13}=78.1538461538\approx78.2$      (2)

Change in mean from (1) and (2)

$\overline{x}_2-\overline{x}_1\\\\=78.2-76.1=2.1$

Hence,  the mean increases by 2.1.

Answer 2

Answer:

When the outlier(s) are removed, how does the mean change?

dot plot with 1 dot over 50, 2 dots over 72, 1 dot over 74, 1 dot over 76, 1 dot over 78, 3 dots over 79, 1 dot over 80, 1 dot over 81, 3 dots over 82, and 1 dot over 83

The mean decreases by 1.9.

The mean increases by 2.4.

The mean increases by 1.9. it's this one.

There are no outliers.

Points earned on this question: 4

Step-by-step explanation: