Calculus Examples

$1$ , $2$ , $4$ , $7$ , $9$ , $10$

Step 1

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

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

Step 2

Simplify the numerator.

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Step 2.1

Add $1$ and $2$ .

$μ = \frac{3 + 4 + 7 + 9 + 10}{6}$

Step 2.2

Add $3$ and $4$ .

$μ = \frac{7 + 7 + 9 + 10}{6}$

Step 2.3

Add $7$ and $7$ .

$μ = \frac{14 + 9 + 10}{6}$

Step 2.4

Add $14$ and $9$ .

$μ = \frac{23 + 10}{6}$

Step 2.5

Add $23$ and $10$ .

$μ = \frac{33}{6}$

Step 3

Cancel the common factor of $33$ and $6$ .

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Step 3.1

Factor $3$ out of $33$ .

$μ = \frac{3 (11)}{6}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $6$ .

$μ = \frac{3 \cdot 11}{3 \cdot 2}$

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