Question

Altering Data Sets: Consider the following data set:

24,    31,    34,    36,    40,    44

Without calculating the statistics, describe what would happen in each case.

(a) The 24 is replaced by a 12.

The mean would decrease.The median would stay the same.    The standard deviation would increase.All of these are true.

(b) The 24 becomes a 22 and the 44 becomes a 46.

The median would increase.The standard deviation would increase.    The mean would increase.All of these are true.

(c) The 36 becomes a 44.

The mean would increase.The mode would now be 44.    The median would change.All of these are true.

Answer 1

a) All of these are true.

The mean would decrease because we replace smaller value than 24

The median does not change because 24 is extreme value which does not affect the extreme observation.

The standard deviation increases because lower value(24) is replace by the more smaller( 12 ) than it.

b) The standard deviation would increase.

Median does not affect the extreme value.

Mean does not change because the addition of 24 and 44 is same as the addition of the new values 22 and 46.

c) All of these are true.

Mean is increase because 44 is greater than 36, so numerator in the formula of mean is increases and so mean is increases.

Mode is the most frequently observation which become 44 , because when we replace 36 by 44 there are two values of 44.

median is change because 36 is one of the middle value and if we replace it by 44 then the next middle value is 40

so the median is increase.