Question

If the maximum value of an observation in the data 5,6,9,10,6,12,3,6,11,10,4,6,7 is changed to 11 would the mode of the data be affected

Answer 1

No, the mode will not be affected. The current mode of the observations is 6, for which there are 4 observations. There is only one observation for 11. So, even in one 6 is changed into a 11, the mode will still be 6.

Answer 2

Changing the maximum value to 11 has no change on the mode, the mode will remain 6.

Given:

a data set: 5, 6, 9, 10, 6, 12, 3, 6, 11, 10, 4, 6, 7

the maximum value in the set is replaced by 11

To Find:

the effect of the change on the mode of the data

Solution:

the mode of a data set is the value that appears the maximum number of times

in the given data, 6 appears 4 times and no other value appears more than 4 times

so, mode = 6

the maximum value in the set is 12

if we replace 12 with 11, the data set becomes: 5, 6, 9, 10, 6, 11, 3, 6, 11, 10, 4, 6, 7

still, 6 appears the maximum number of times

Thus, changing the maximum value to 11 has no change on the mode, the mode will remain 6.

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