Explore if it is possible to include or remove 2 values such that the mean is unchanged. Class 8

Explore if it is possible to include or remove 2 values such that the mean is unchanged. Class 8

Question 1.

Explore if it is possible to include or remove 2 values such that the mean is unchanged. Class 8

You may use the following data to experiment with.

Solution:

Here, mean

= 3 + 5 + 6.5 + 7 + 7.5 + 4 × 8 + 9 + 2 × 10 + 11 + 2 × 12 + 13 + 15

= [latex]\frac{153}{17}[/latex] = 9.

If we remove 5 and 13, then mean will be [latex]\frac{153-18}{15}[/latex] = [latex]\frac{135}{15}[/latex] = 9.

Similarly, if we remove 8 and 10, then mean will be [latex]\frac{153-18}{15}[/latex] = [latex]\frac{135}{15}[/latex] = 9.

So, it is possible in this case.

Question 2.

We saw what happens to the mean when values are included or removed from the collection. What happens to the mean if every value in the collection increases by some fixed number? Class 8

Solution:

Mean may increase or decrease or remains the same, depending on the values including or removed. If every value in the collection is increased by a fixed number, then the mean will increased by the same fixed number.