Calculus Examples

$10$ , $74$ , $78$ , $102$

Step 1

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

$μ = \frac{10 + 74 + 78 + 102}{4}$

Step 2

Cancel the common factor of $10 + 74 + 78 + 102$ and $4$ .

Tap for more steps...

Step 2.1

Factor $2$ out of $10$ .

$μ = \frac{2 (5) + 74 + 78 + 102}{4}$

Step 2.2

Factor $2$ out of $74$ .

$μ = \frac{2 \cdot 5 + 2 \cdot 37 + 78 + 102}{4}$

Step 2.3

Factor $2$ out of $2 \cdot 5 + 2 \cdot 37$ .

$μ = \frac{2 \cdot (5 + 37) + 78 + 102}{4}$

Step 2.4

Factor $2$ out of $78$ .

$μ = \frac{2 \cdot (5 + 37) + 2 (39) + 102}{4}$

Step 2.5

Factor $2$ out of $2 \cdot (5 + 37) + 2 (39)$ .

$μ = \frac{2 \cdot (5 + 37 + 39) + 102}{4}$

Step 2.6

Factor $2$ out of $102$ .

$μ = \frac{2 \cdot (5 + 37 + 39) + 2 (51)}{4}$

Step 2.7

Factor $2$ out of $2 \cdot (5 + 37 + 39) + 2 (51)$ .

$μ = \frac{2 \cdot (5 + 37 + 39 + 51)}{4}$

Step 2.8

Cancel the common factors.

Tap for more steps...

Step 2.8.1

Factor $2$ out of $4$ .

$μ = \frac{2 \cdot (5 + 37 + 39 + 51)}{2 (2)}$

Step 2.8.2

Cancel the common factor.

$μ = \frac{2 \cdot (5 + 37 + 39 + 51)}{2 \cdot 2}$

Step 2.8.3

Rewrite the expression.

$μ = \frac{5 + 37 + 39 + 51}{2}$

Step 3

Simplify the numerator.

Tap for more steps...

Step 3.1

Add $5$ and $37$ .

$μ = \frac{42 + 39 + 51}{2}$

Step 3.2

Add $42$ and $39$ .

$μ = \frac{81 + 51}{2}$

Step 3.3

Add $81$ and $51$ .

$μ = \frac{132}{2}$

Step 4

Divide $132$ by $2$ .

$μ = 66$

Step 5

Arrange the terms in ascending order.

$M e d i a n = 10, 74, 78, 102$

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.

$M e d i a n = \frac{74 + 78}{2}$

Step 7

Remove parentheses.

$M e d i a n = \frac{74 + 78}{2}$

Step 8

Cancel the common factor of $74 + 78$ and $2$ .

Tap for more steps...

Step 8.1

Factor $2$ out of $74$ .

$M e d i a n = \frac{2 \cdot 37 + 78}{2}$

Step 8.2

Factor $2$ out of $78$ .

$M e d i a n = \frac{2 \cdot 37 + 2 \cdot 39}{2}$

Step 8.3

Factor $2$ out of $2 \cdot 37 + 2 \cdot 39$ .

$M e d i a n = \frac{2 \cdot (37 + 39)}{2}$

Step 8.4

Cancel the common factors.

Tap for more steps...

Step 8.4.1

Factor $2$ out of $2$ .

$M e d i a n = \frac{2 \cdot (37 + 39)}{2 (1)}$

Step 8.4.2

Cancel the common factor.

$M e d i a n = \frac{2 \cdot (37 + 39)}{2 \cdot 1}$

Step 8.4.3

Rewrite the expression.

$M e d i a n = \frac{37 + 39}{1}$

Step 8.4.4

Divide $37 + 39$ by $1$ .

$M e d i a n = 37 + 39$

Step 9

Add $37$ and $39$ .

$M e d i a n = 76$

Step 10

Convert the median $76$ to decimal.

$M e d i a n = 76$

Step 11

Since the mean is less than the median, the data set is negatively skewed.

Negatively Skewed