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 = [tex]\overline{x}_1=\dfrac{\text{Sum of observations}}{\text{No. of observations}}[/tex] (1)
[tex]=\dfrac{1066}{14}=76.1428571429\approx76.1[/tex]
First Quartile: [tex]Q_1=[/tex] Median of the lower half ( 50 , 72, 72 , 74, 76 , 78 , 79 )
= 74
Third Quartile: [tex]Q_3=[/tex] Median of the upper half ( 79 , 79 80, 81, 82, 82, 82 )
= 81
Interquartile range (IQR)=[tex]Q_3-Q_1=81-74=7[/tex]
According to the IQR rule,
Upper limit = [tex]1.5\times IQR+Q_3=1.5\times7+81=91.5[/tex]
Lower limit = [tex]Q_1-1.5\times IQR=74-1.5\times7=63.5[/tex]
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 = [tex]\overline{x}_2=\dfrac{\text{Sum of observations}}{\text{No. of observations}}[/tex]
[tex]=\dfrac{1016}{13}=78.1538461538\approx78.2[/tex] (2)
Change in mean from (1) and (2)
[tex]\overline{x}_2-\overline{x}_1\\\\=78.2-76.1=2.1[/tex]
Hence, the mean increases by 2.1.
