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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

User Paxer
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Answer:

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.

User Ascobol
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