Score that will yield a Given Mean

Introduction

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.

Example 1

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 = (8+12+8+10+18+12+4+x)8 = 11

= 72 + x = 88; x = 88 72 = 16

Step 3:

Required new score = 16.

Example 2

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 = (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