- Mean, Median, and Mode
- Home
- Mode of a Data Set
- Finding the Mode and Range of a Data Set
- Finding the Mode and Range from a Line Plot
- Mean of a Data Set
- Understanding the Mean Graphically: Two bars
- Understanding the Mean Graphically: Four or more bars
- Finding the Mean of a Symmetric Distribution
- Computations Involving the Mean, Sample Size, and Sum of a Data Set
- Finding the Value for a New Score that will yield a Given Mean
- Mean and Median of a Data Set
- How Changing a Value Affects the Mean and Median
- Finding Outliers in a Data Set
- Choosing the Best Measure to Describe Data

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

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