Statistics Examples

$2$ , $4$ , $6$ , $8$ , $10$ , $12$ , $14$

Step 1

There are $7$ observations, so the median is the middle number 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.

$2, 4, 6, 8, 10, 12, 14$

Step 3

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

$8$

Step 4

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

$2, 4, 6$

Step 5

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

$4$

Step 6

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

$10, 12, 14$

Step 7

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

$12$

Step 8

The midhinge is the average of the first and third quartiles.

$Midhinge = \frac{Q_{1} + Q_{3}}{2}$

Step 9

Substitute the values for the first quartile $4$ and the third quartile $12$ into the formula.

$Midhinge = \frac{4 + 12}{2}$

Step 10

Simplify $\frac{4 + 12}{2}$ to find the midhinge.

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Step 10.1

Cancel the common factor of $4 + 12$ and $2$ .

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Step 10.1.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 2 + 12}{2}$

Step 10.1.2

Factor $2$ out of $12$ .

$\frac{2 \cdot 2 + 2 \cdot 6}{2}$

Step 10.1.3

Factor $2$ out of $2 \cdot 2 + 2 \cdot 6$ .

$\frac{2 \cdot (2 + 6)}{2}$

Step 10.1.4

Cancel the common factors.

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Step 10.1.4.1

Factor $2$ out of $2$ .

$\frac{2 \cdot (2 + 6)}{2 (1)}$

Step 10.1.4.2

Cancel the common factor.

$\frac{2 \cdot (2 + 6)}{2 \cdot 1}$

Step 10.1.4.3

Rewrite the expression.

$\frac{2 + 6}{1}$

Step 10.1.4.4

Divide $2 + 6$ by $1$ .

$2 + 6$

Step 10.2

Add $2$ and $6$ .

$8$