How Changing a Value Affects the Mean and Median Online Quiz
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Q 1 - Find new mean and new median of the data set if a data is changed.
17 , 7 , 2 , 15 , 6 , 19 , 20 , 15 , 18; 2 is changed to 12
Answer : C
Explanation
Step 1:
Mean = $\frac{(17 + 7 + 2 + 15 + 6 + 19 + 20 + 15 + 18)}{9}$ = 13.22; Median = 15
Step 2:
With data change
New Mean = $\frac{(17 + 7 + 12 + 15 + 6 + 19 + 20 + 15 + 18)}{9}$ = 14.33; New Median = 15.
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Q 2 - Find new mean and new median of the data set if a data is changed.
12 , 15 , 18 , 13 , 6 , 14; 13 is changed to 5
Answer : D
Explanation
Step 1:
Mean = $\frac{(12 + 15 + 18 + 13 + 6 + 14 )}{6}$ = 13; Median = 13.5
Step 2:
With data change
New Mean = $\frac{(12 + 15 + 18 + 5 + 6 + 14 )}{6}$ = 11.67; New Median = 13
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Q 3 - Find new mean and new median of the data set if a data is changed.
18 , 7 , 11 , 1 , 19 , 15 , 19 , 9; 7 is changed to 14
Answer : A
Explanation
Step 1:
Mean = $\frac{(18 + 7 + 11 + 1 + 19 + 15 + 19 + 9 +7)}{9}$ = 12.38; Median = 13
Step 2:
With data change
New Mean = $\frac{(18 + 14 + 11 + 1 + 19 + 15 + 19 + 9 +7)}{9}$ = 13.25 ; New Median = 14.5
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Q 4 - Find new mean and new median of the data set if a data is changed.
8 , 12 , 8 , 10 , 18 , 12 , 4; 10 is changed to 17
Answer : B
Explanation
Step 1:
Mean = $\frac{(8 + 12 + 8 + 10 + 18 + 12 + 4)}{7}$ = 10.29; Median = 10
Step 2:
With data change
New Mean = $\frac{(8 + 12 + 8 + 17 + 18 + 12 + 4)}{7}$ = 11.29; New Median = 12
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Q 5 - Find new mean and new median of the data set if a data is changed.
20 , 5 , 7 , 6 , 19 , 5 , 16 , 7; 20 is changed to 10
Answer : C
Explanation
Step 1:
Mean = $\frac{(20 + 5 + 7 + 6 + 19 + 5 + 16 + 7)}{8}$ = 10.63; Median = 7
Step 2:
With data change
New Mean = $\frac{(10 + 5 + 7 + 6 + 19 + 5 + 16 + 7)}{8}$ = 9.38; New Median = 7
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Q 6 - Find new mean and new median of the data set if a data is changed.
12 , 12 , 4 , 12 , 2 , 12; 4 is changed to 8
Answer : A
Explanation
Step 1:
Mean = $\frac{(12 + 12 + 4 + 12 + 2 + 12)}{6}$ = 9; Median = 12
Step 2:
With data change
New Mean = $\frac{(12 + 12 + 8 + 12 + 2 + 12)}{6}$ = 9.67; New Median = 12
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Q 7 - Find new mean and new median of the data set if a data is changed.
6 , 12 , 9 , 4 , 4; 12 is changed to 15
Answer : B
Explanation
Step 1:
Mean = $\frac{(6 + 12 + 9 + 4 + 4 )}{5}$ = 7; Median = 6
Step 2:
New Mean = $\frac{(6 + 15 + 9 + 4 + 4)}{5}$ = 7.6 ; New Median = 6
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Q 8 - Find new mean and new median of the data set if a data is changed.
18 , 15 , 11 , 3 , 8 , 4 , 13 , 12 , 3; 15 is changed to 18
Answer : D
Explanation
Step 1:
Mean = $\frac{(18 + 15 + 11 + 3 + 8 + 4 + 13 + 12 +3)}{9}$ = 9.67; Median = 11
Step 2:
With data change
New Mean = $\frac{(18 + 18 + 11 + 3 + 8 + 4 + 13 + 12 +3)}{9}$ = 10; New Median = 11
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Q 9 - Find new mean and new median of the data set if a data is changed.
25 , 18 , 18 , 13 , 4 , 17 , 18 , 19 , 3; 4 is changed to 9
Answer : A
Explanation
Step 1:
Mean = $\frac{(25 + 18 + 18 + 13 + 4 + 17 + 18 + 19 +3)}{9}$ = 15; Median = 18
Step 2:
With data change
New Mean = $\frac{(25 + 18 + 18 + 13 + 9 + 17 + 18 + 19 +3)}{9}$ = 15.55; New Median = 18
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Q 10 - Find new mean and new median of the data set if a data is changed
21 , 1 , 16 , 8 , 19; 1 is changed to 5
Answer : C
Explanation
Step 1:
Mean = $\frac{(21 + 1 + 16 + 8 + 19)}{5}$ = 13 ; Median = 16
Step 2:
With data change
New Mean = $\frac{(21 + 1 + 16 + 8 + 19)}{5}$ = 13.8; New Median = 16
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