Basic Math Examples

12

$12$ ,

15

$15$ ,

9

$9$ ,

5

$5$ ,

17

$17$ ,

16

$16$ ,

10

$10$ ,

11

$11$ ,

4

$4$ ,

8

$8$ ,

9

$9$ ,

20

$20$ ,

12

$12$

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

$M$ - the middle term

4. First Quartile

Q_{1}

$Q_{1}$ - the middle term of values below the median

5. Third Quartile

Q_{3}

$Q_{3}$ - the middle term of values above the median

Step 2

Arrange the terms in ascending order.

4, 5, 8, 9, 9, 10, 11, 12, 12, 15, 16, 17, 20

$4, 5, 8, 9, 9, 10, 11, 12, 12, 15, 16, 17, 20$

Step 3

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

4

$4$

Step 4

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

20

$20$

Step 5

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

11

$11$

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.

4, 5, 8, 9, 9, 10

$4, 5, 8, 9, 9, 10$

Step 6.2

The median for the lower half of data

4, 5, 8, 9, 9, 10

$4, 5, 8, 9, 9, 10$ is the lower or first quartile. In this case, the first quartile is

8.5

$8.5$ .

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Step 6.2.1

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{8 + 9}{2}

$\frac{8 + 9}{2}$

Step 6.2.2

Remove parentheses.

\frac{8 + 9}{2}

$\frac{8 + 9}{2}$

Step 6.2.3

Add

8

$8$ and

9

$9$ .

\frac{17}{2}

$\frac{17}{2}$

Step 6.2.4

Convert the median

\frac{17}{2}

$\frac{17}{2}$ to decimal.

8.5

$8.5$

8.5

$8.5$

8.5

$8.5$

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.

12, 12, 15, 16, 17, 20

$12, 12, 15, 16, 17, 20$

Step 7.2

The median for the upper half of data

12, 12, 15, 16, 17, 20

$12, 12, 15, 16, 17, 20$ is the upper or third quartile. In this case, the third quartile is

15.5

$15.5$ .

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Step 7.2.1

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{15 + 16}{2}

$\frac{15 + 16}{2}$

Step 7.2.2

Remove parentheses.

\frac{15 + 16}{2}

$\frac{15 + 16}{2}$

Step 7.2.3

Add

15

$15$ and

16

$16$ .

\frac{31}{2}

$\frac{31}{2}$

Step 7.2.4

Convert the median

\frac{31}{2}

$\frac{31}{2}$ to decimal.

15.5

$15.5$

15.5

$15.5$

15.5

$15.5$

Step 8

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

Min = 4

$Min = 4$

Max = 20

$Max = 20$

M = 11

$M = 11$

Q_{1} = 8.5

$Q_{1} = 8.5$

Q_{3} = 15.5

$Q_{3} = 15.5$