Finite Math Examples

$1$ , $2$ , $3$ , $4$ , $5$ , $6$ , $7$ , $8$ , $9$ , $10$

Step 1

There are $10$ 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.

$1, 2, 3, 4, 5, 6, 7, 8, 9, 10$

Step 3

Find the median of $1, 2, 3, 4, 5, 6, 7, 8, 9, 10$ .

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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.

$\frac{5 + 6}{2}$

Step 3.2

Remove parentheses.

$\frac{5 + 6}{2}$

Step 3.3

Add $5$ and $6$ .

$\frac{11}{2}$

Step 3.4

Convert the median $\frac{11}{2}$ to decimal.

$5.5$

Step 4

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

$1, 2, 3, 4, 5$

Step 5

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

$3$

Step 6

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

$6, 7, 8, 9, 10$

Step 7

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

$8$

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 $3$ and the third quartile $8$ into the formula.

$Midhinge = \frac{3 + 8}{2}$

Step 10

Add $3$ and $8$ .

$\frac{11}{2}$

Step 11

The midhinge is the average of the first and third quartiles. In this case, the midhinge is $\frac{11}{2}$ , which is approximately $5.5$ .

Exact midhinge: $\frac{11}{2}$

Approximate midhinge: $5.5$

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