Consider the following data set: 26, 30, 33, 35, 40, 44 Without calculating the

Question

Consider the following data set: 26, 30, 33, 35, 40, 44

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

(a) The 26 is replaced by a 13.

The mean would decrease.

The median would stay the same.

The standard deviation would increase.

All of these are true.

(b) The 26 becomes a 24 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 35 becomes a 44.

The mean would increase.

The mode would now be 44.

The median would change.

All of these are true.

Explanation / Answer

Mean : Mean is average of all data values.

Average is sum of all data values devided by n.

Median : Median is the middle value of the data if data is arranged in ascending order.

Standard deviation : Standard deviation is square root of the average of squared deviations from mean.

a)

Here the value13 is less than 26 . If the 26 is replaced by a 13, average will also decrease.

While calculating median 26 was the smallest value in the data. If it is replaced by 13, then also 13 will be the smallest value in the data.

Hence median will same.

Looking at the data set 13 will increase the deviation in the data, hence the standard deviation would increase.

The correct option is :

All of these are true.

B) Here the 26 becomes a 24 and the 44 becomes a 46.

Here sum of data values will not change. Hence the average will also be not change.

Here 26 and 44 are extreme data values , change in these data values will remain still extreme. Hence median will also be the same.

Here 26 is reduced by 2 and 44 is incrased by 2. Hence here variation is increased.

The correct option is

The standard deviation would increase.

c) Here the 35 becomes a 44.

Hence position of 35 will take 40 . Hence value of median will increase.

As 35 become 44, that is value increased , mean is also increased.

Now in the data set value 44 is repeated. Hence mode is 44.

Hence the correct option is All of these are true.

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