How Changing a Value Affects the Mean and Median Online Quiz

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Questions and Answers
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.

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

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

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

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

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

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

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

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

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

how_changing_value_affects_mean_and_median.htm
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