The mean of the new collection also increases by 10. Notice that the relative position of the mean stays the same. Class 8

The mean of the new collection also increases by 10. Notice that the relative position of the mean stays the same. Class 8

Question 1.

The mean of the new collection also increases by 10. Notice that the relative position of the mean stays the same. Class 8

We get the following dot plot if we reduce every value by 1.

Solution:

Mean

= [latex]\frac{12+13+14+15+2 \times 16+3 \times 17+19+22}{11}[/latex]

= [latex]\frac{178}{11}[/latex] = 16.18.

Thus, mean also reduces by 1.

Question 2.

Try to explain, using algebra, what the average is when a fixed number, e.g., 2 is subtracted from every value in the collection. Class 8

Solution:

Let the given values are x₁, x₂, x₃,..., x_n.

So, their average = [latex]\frac{x_1+x_2+x_3+\ldots+x_n}{n}[/latex]

After a reduction of 2 from each value, the new average

Thus, new average has reduced by 2.