Finite Math Examples Average Descriptive Statistics

Find the Five Number Summary

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

Step 1

The five-number summary is a descriptive statistic that provides information about a set of observations. It consists of the following statistics:

1. Minimum (Min) - the smallest observation

2. Maximum (Max) - the largest observation

3. Median $M$ - the middle term

4. First Quartile $Q_{1}$ - the middle term of values below the median

5. Third Quartile $Q_{3}$ - the middle term of values above the median

Step 2

Arrange the terms in ascending order.

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

Step 3

The minimum value is the smallest value in the arranged data set.

$11$

Step 4

The maximum value is the largest value in the arranged data set.

$77$

Step 5

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

$41$

Step 6

Find the first quartile by finding the median of the set of values to the left of the median.

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Step 6.1

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

$11, 14, 14, 17, 17$

Step 6.2

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

$14$

Step 7

Find the third quartile by finding the median of the set of values to the right of the median.

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Step 7.1

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

$44, 47, 71, 74, 77$

Step 7.2

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

$71$

Step 8

The five most important sample values are sample minimum, sample maximum, median, lower quartile, and upper quartile.

$Min = 11$

$Max = 77$

$M = 41$

$Q_{1} = 14$

$Q_{3} = 71$

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Average Descriptive Statistics

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