# Finding the Mean of a Symmetric Distribution Online Quiz

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Q 1 - Find the mean of the following symmetric distribution.

2, 2, 4, 4, 5, 5, 6, 6, 8, 8

### Explanation

Step 1:

Mean of distribution = $\frac{(2 + 2 + 4 + 4 + 5 + 5 + 6 + 6 + 8 + 8)}{10} = \frac{50}{10}$ = 5

Step 2:

Or mean of middle two numbers = $\frac{(5 + 5)}{2}$ = 5

So mean of symmetric distribution = 5

Q 2 - Find the mean of the following symmetric distribution.

0, 0, 3, 3, 5, 7, 9, 9, 12, 12

### Explanation

Step 1:

Mean of distribution = $\frac{(0 + 0 + 3 + 3 + 5 + 7 + 9 + 9 + 12 + 12)}{10} = \frac{60}{10}$ = 6

Step 2:

Or mean of middle two numbers = $\frac{(5 + 7)}{2}$ = 6

So, mean of symmetric distribution = 6

Q 3 - Find the mean of the following symmetric distribution.

1, 1, 4, 4, 5, 6, 7, 7, 10, 10

### Explanation

Step 1:

Mean of distribution = $\frac{(1 + 1 + 4 + 4 + 5 + 6 + 7 + 7 + 10 + 10)}{10} = \frac{55}{10}$ = 5.5

Step 2:

Or mean of middle two numbers = $\frac{(5 + 6)}{2}$ = 5.5

So mean of symmetric distribution = 5.5

Q 4 - Find the mean of the following symmetric distribution.

0, 0, 2, 2, 3, 4, 5, 5, 7, 7

### Explanation

Step 1:

Mean of distribution = $\frac{(0 + 0 + 2 + 2 + 3 + 4 + 5 + 5 + 7 + 7)}{10} = \frac{35}{10}$ = 3.5

Step 2:

Or mean of middle two numbers = $\frac{(3 + 4)}{2}$ = 3.5

So mean of symmetric distribution = 3.5

Q 5 - Find the mean of the following symmetric distribution.

3, 3, 5, 5, 6, 6, 7, 7, 9, 9

### Explanation

Step 1:

Mean of distribution = $\frac{(3 + 3 + 5 + 5 + 6 + 6 + 7 + 7 + 9 + 9)}{10} = \frac{60}{10}$ = 6

Step 2:

Or mean of middle two numbers = $\frac{(6 + 6)}{2}$ = 6

So mean of symmetric distribution = 6

Q 6 - Find the mean of the following symmetric distribution.

3, 3, 5, 5, 6, 7, 8, 8, 10, 10

### Explanation

Step 1:

Mean of distribution = $\frac{(3 + 3 + 5 + 5 + 6 + 7 + 8 + 8 + 10 + 10)}{10} = \frac{65}{10}$ = 6.5

Step 2:

Or mean of middle two numbers = $\frac{(6 + 7)}{2}$ = 6.5

So, mean of symmetric distribution = 6.5

Q 7 - Find the mean of the following symmetric distribution.

1, 1, 3, 3, 4, 4, 5, 5, 7, 7

### Explanation

Step 1:

Mean of distribution = $\frac{(1 + 1 + 3 + 3 + 4 + 4 + 5 + 5 + 7 + 7)}{10} = \frac{40}{10}$ = 4

Step 2:

Or mean of middle two numbers = $\frac{(4 + 4)}{2}$ = 4

Mean of symmetric distribution = 4

Q 8 - Find the mean of the following symmetric distribution.

2, 2, 4, 4, 5, 6, 7, 7, 9, 9

### Explanation

Step 1:

Mean of distribution = $\frac{(2 + 2 + 4 + 4 + 5 + 6 + 7 + 7 + 9 + 9)}{10} = \frac{55}{10}$ = 5.5

Step 2:

Or mean of middle two numbers = $\frac{(5 + 6)}{2}$ = 5.5

So mean of symmetric distribution = 5.5

Q 9 - Find the mean of the following symmetric distribution.

3, 3, 5, 5, 6, 7, 8, 8, 10, 10

### Explanation

Step 1:

Mean of distribution = $\frac{(3 + 3 + 5 + 5 + 6 + 7 + 8 + 8 + 10 + 10)}{10} = \frac{65}{10}$ = 6.5

Step 2:

Or mean of middle two numbers = $\frac{(6 + 7)}{2}$ = 6.5

So mean of symmetric distribution = 6.5

Q 10 - Find the mean of the following symmetric distribution.

1, 1, 3, 3, 4, 5, 6, 6, 8, 8

### Explanation

Step 1:

Mean of distribution = $\frac{(1 + 1 + 3 + 3 + 4 + 5 + 6 + 6 + 8 + 8)}{10} = \frac{45}{10}$ = 4.5

Step 2:

Or mean of middle two numbers = $\frac{(4 + 5)}{2}$ = 4.5

So mean of symmetric distribution = 4.5

finding_mean_of_symmetric_distribution.htm