Statistics Examples

1

$1$ ,

2

$2$ ,

4

$4$ ,

7

$7$ ,

9

$9$ ,

10

$10$

Step 1

The mean of a set of numbers is the sum divided by the number of terms.

μ = \frac{1 + 2 + 4 + 7 + 9 + 10}{6}

$μ = \frac{1 + 2 + 4 + 7 + 9 + 10}{6}$

Step 2

Simplify the numerator.

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Step 2.1

Add

1

$1$ and

2

$2$ .

μ = \frac{3 + 4 + 7 + 9 + 10}{6}

$μ = \frac{3 + 4 + 7 + 9 + 10}{6}$

Step 2.2

Add

3

$3$ and

4

$4$ .

μ = \frac{7 + 7 + 9 + 10}{6}

$μ = \frac{7 + 7 + 9 + 10}{6}$

Step 2.3

Add

7

$7$ and

7

$7$ .

μ = \frac{14 + 9 + 10}{6}

$μ = \frac{14 + 9 + 10}{6}$

Step 2.4

Add

14

$14$ and

9

$9$ .

μ = \frac{23 + 10}{6}

$μ = \frac{23 + 10}{6}$

Step 2.5

Add

23

$23$ and

10

$10$ .

μ = \frac{33}{6}

$μ = \frac{33}{6}$

μ = \frac{33}{6}

$μ = \frac{33}{6}$

Step 3

Cancel the common factor of

33

$33$ and

6

$6$ .

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Step 3.1

Factor

3

$3$ out of

33

$33$ .

μ = \frac{3 (11)}{6}

$μ = \frac{3 (11)}{6}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

3

$3$ out of

6

$6$ .

μ = \frac{3 \cdot 11}{3 \cdot 2}

$μ = \frac{3 \cdot 11}{3 \cdot 2}$

Step 3.2.2

Cancel the common factor.

$μ = \frac{3 \cdot 11}{3 \cdot 2}$

Step 3.2.3

Rewrite the expression.

$μ = \frac{11}{2}$

Step 4

Divide.

$μ = 5.5$

Step 5

Arrange the terms in ascending order.

$M e d i a n = 1, 2, 4, 7, 9, 10$

Step 6

The median is the middle term in the arranged data set. In the case of an even number of terms, the median is the average of the two middle terms.

$M e d i a n = \frac{4 + 7}{2}$

Step 7

Remove parentheses.

$M e d i a n = \frac{4 + 7}{2}$

Step 8

Add

$4$ and

$7$ .

$M e d i a n = \frac{11}{2}$

Step 9

Convert the median

$\frac{11}{2}$ to decimal.

$M e d i a n = 5.5$

Step 10

Since the mean is equal to the median, the data set is symmetric.

Symmetric

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