Question

Find the values of the measures shown when each value in the data set increases by 25. Mean: 109 Median: 104 Mode: 96 Range: 45 Standard deviation: 3.6

Answer 1

The new values are as follows:

Mean: 134

Median: 129

Mode: 121

Range=45

Standard Deviation=3.6

Explanation:

When a k real number is added to all the elements of the dataset, the new measures of center (mean, median, and mode) are simply found by adding the value k to the previous values. Thus

`Mean_(new)=Mean_(old)+k`

Here
`Mean_(old)` is 109 and k is 25 thus

`Mean_(new)=Mean_(old)+k\\Mean_(new)=109+25\\Mean_(new)=134`

Similarly

`Median_(new)=Median_(old)+k`

Here
`Median_(old)` is 104 and k is 25 thus

`Median_(new)=Median_(old)+k\\Median_(new)=104+25\\Median_(new)=129`

Also

`Mode_(new)=Mode_(old)+k`

Here
`Mode_(old)` is 96 and k is 25 thus

`Mode_(new)=Mode_(old)+k\\Mode_(new)=96+25\\Mode_(new)=121`

When a k real number is added to all the elements of the dataset, the new measures of variation (range and standard deviation) remain the same thus.

`Range_(new)=Range_(old)\\Range_(new)=45`

Similarly

`Standard\ Deviation_(new)=Standard\ Deviation_(old)\\Standard\ Deviation_(new)=3.6`

So the new values of mean, median, mode, range, and standard deviation are 134, 129, 121, 45, and 3.6 respectively.