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Yuri [45]
2 years ago
10

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
Mathematics
1 answer:
Vikki [24]2 years ago
4 0

Answer:

The new values are as follows:

Mean: 134

Median: 129

Mode: 121

Range=45

Standard Deviation=3.6

Step-by-step 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.

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