Calculus Examples

$11$ , $14$ , $14$ , $17$ , $17$ , $17$ , $41$ , $44$ , $47$ , $71$ , $74$ , $77$

Step 1

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

$μ = \frac{11 + 14 + 14 + 17 + 17 + 17 + 41 + 44 + 47 + 71 + 74 + 77}{12}$

Step 2

Simplify the numerator.

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Step 2.1

Add $11$ and $14$ .

$μ = \frac{25 + 14 + 17 + 17 + 17 + 41 + 44 + 47 + 71 + 74 + 77}{12}$

Step 2.2

Add $25$ and $14$ .

$μ = \frac{39 + 17 + 17 + 17 + 41 + 44 + 47 + 71 + 74 + 77}{12}$

Step 2.3

Add $39$ and $17$ .

$μ = \frac{56 + 17 + 17 + 41 + 44 + 47 + 71 + 74 + 77}{12}$

Step 2.4

Add $56$ and $17$ .

$μ = \frac{73 + 17 + 41 + 44 + 47 + 71 + 74 + 77}{12}$

Step 2.5

Add $73$ and $17$ .

$μ = \frac{90 + 41 + 44 + 47 + 71 + 74 + 77}{12}$

Step 2.6

Add $90$ and $41$ .

$μ = \frac{131 + 44 + 47 + 71 + 74 + 77}{12}$

Step 2.7

Add $131$ and $44$ .

$μ = \frac{175 + 47 + 71 + 74 + 77}{12}$

Step 2.8

Add $175$ and $47$ .

$μ = \frac{222 + 71 + 74 + 77}{12}$

Step 2.9

Add $222$ and $71$ .

$μ = \frac{293 + 74 + 77}{12}$

Step 2.10

Add $293$ and $74$ .

$μ = \frac{367 + 77}{12}$

Step 2.11

Add $367$ and $77$ .

$μ = \frac{444}{12}$

Step 3

Divide $444$ by $12$ .

$μ = 37$

Step 4

Arrange the terms in ascending order.

$M e d i a n = 11, 14, 14, 17, 17, 17, 41, 44, 47, 71, 74, 77$

Step 5

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.

$M e d i a n = \frac{17 + 41}{2}$

Step 6

Remove parentheses.

$M e d i a n = \frac{17 + 41}{2}$

Step 7

Add $17$ and $41$ .

$M e d i a n = \frac{58}{2}$

Step 8

Divide $58$ by $2$ .

$M e d i a n = 29$

Step 9

Convert the median $29$ to decimal.

$M e d i a n = 29$

Step 10

Since the mean is greater than the median, the data set is positively skewed.

Positively Skewed