Trigonometry Examples

$28.2$ , $29.3$ , $29.7$ , $31.6$ , $31.7$ , $32.7$ , $32.8$ , $33.5$ , $33.5$ , $33.5$ , $33.8$ , $34.2$ , $34.8$ , $34.8$ , $35.4$ , $36.7$ , $37.3$ , $38.5$

Step 1

There are $18$ observations, so the median is the mean of the two middle numbers of the arranged set of data. Splitting the observations either side of the median gives two groups of observations. The median of the lower half of data is the lower or first quartile. The median of the upper half of data is the upper or third quartile.

The median of the lower half of data is the lower or first quartile

The median of the upper half of data is the upper or third quartile

Step 2

Arrange the terms in ascending order.

$28.2, 29.3, 29.7, 31.6, 31.7, 32.7, 32.8, 33.5, 33.5, 33.5, 33.8, 34.2, 34.8, 34.8, 35.4, 36.7, 37.3, 38.5$

Step 3

Find the median of $28.2, 29.3, 29.7, 31.6, 31.7, 32.7, 32.8, 33.5, 33.5, 33.5, 33.8, 34.2, 34.8, 34.8, 35.4, 36.7, 37.3, 38.5$ .

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Step 3.1

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.

$\frac{33.5 + 33.5}{2}$

Step 3.2

Simplify the expression.

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Step 3.2.1

Remove parentheses.

$\frac{33.5 + 33.5}{2}$

Step 3.2.2

Add $33.5$ and $33.5$ .

$\frac{67}{2}$

Step 3.3

Cancel the common factor of $67$ and $2$ .

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Step 3.3.1

Rewrite $67$ as $1 (67)$ .

$\frac{1 (67)}{2}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Rewrite $2$ as $1 (2)$ .

$\frac{1 \cdot 67}{1 \cdot 2}$

Step 3.3.2.2

Cancel the common factor.

$\frac{1 \cdot 67}{1 \cdot 2}$

Step 3.3.2.3

Rewrite the expression.

$\frac{67}{2}$

Step 3.4

Convert the median $\frac{67}{2}$ to decimal.

$33.5$

Step 4

The lower half of data is the set below the median.

$28.2, 29.3, 29.7, 31.6, 31.7, 32.7, 32.8, 33.5, 33.5$

Step 5

The median is the middle term in the arranged data set.

$31.7$

Step 6

The upper half of data is the set above the median.

$33.5, 33.8, 34.2, 34.8, 34.8, 35.4, 36.7, 37.3, 38.5$

Step 7

The median is the middle term in the arranged data set.

$34.8$

Step 8

The interquartile range is the difference between the first quartile $31.7$ and the third quartile $34.8$ . In this case, the difference between the first quartile $31.7$ and the third quartile $34.8$ is $34.8 - (31.7)$ .

$34.8 - (31.7)$

Step 9

Simplify $34.8 - (31.7)$ .

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Step 9.1

Multiply $- 1$ by $31.7$ .

$34.8 - 31.7$

Step 9.2

Subtract $31.7$ from $34.8$ .

$3.1$