# Finding the Value for a New Score that will yield a Given Mean

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In this lesson, we are given a data set. We are given a new mean of the data set and are required find a new data member which when added will yield the new mean of the changed data set.

## Rules to find new score that will yield a new given mean

• We start by taking the new score as x.

• We add x to the sum of data to find the new sum of data.

• If the number of data were ‘n’, now we have ‘n+1’ as the new number of data.

• Equating new sum of data divided by ‘n+1’ to the new mean and solving we find the value of new score x.

Find the value for a new score that will yield a given mean.

8, 12, 8, 10, 18, 12, 4; New mean = 11

### Solution

Step 1:

Let the new score to be added = x

Step 2:

New mean = $\frac{(8 + 12 + 8 + 10 + 18 + 12 + 4 + x )}{8}$ = 11

= 72 + x = 88; x = 88 – 72 = 16

Step 3:

Required new score = 16.

Find the value for a new score that will yield a given mean.

25, 18, 18, 13, 4, 17, 18, 19, 3; New mean = 17

### Solution

Step 1:

Let the new score to be added = x

Step 2:

New mean = $\frac{(25 + 18 + 18 + 13 + 4 + 17 + 18 + 19 + 3 + x )}{10}$ = 17

= 135 + x = 170; x = 170 – 135 = 35

Step 3:

Required new score = 35