Finding the median from a frequency table Revision Card

AI generatedStatisticsKey Stage 3

Finding the median from a frequency table.

Put values in order or use cumulative frequencies.
For an odd count, choose the middle observation. For an even count, average the two middle observations.
A median class identifies an interval, not the exact median.

Example 1

Find the median.

Given information

Value	Frequency
1	2
2	3
3	5
4	2

Locate the middle observation(s)

Value	Frequency	Cumulative frequency
1	2	2
2	3	5
3	5	10
4	2	12
Total	12

Black: given data. Blue: working we add.

Add the frequencies to count all observations.

Middle position(s)

Use the two middle positions for an even total, and the single middle position for an odd total.

Median

Read the values at those positions, then average if there are two.

Example 2

Find the median.

Given information

Value	Frequency
2	3
3	3
4	6
5	2

Locate the middle observation(s)

Value	Frequency	Cumulative frequency
2	3	3
3	3	6
4	6	12
5	2	14
Total	14

Black: given data. Blue: working we add.

Add the frequencies to count all observations.

Middle position(s)

Use the two middle positions for an even total, and the single middle position for an odd total.

Median

Read the values at those positions, then average if there are two.

Your turn

Question 1

Find the median.

Given information

Value	Frequency
3	4
4	3
5	7
6	2

Check answer

Locate the middle observation(s)

Value	Frequency	Cumulative frequency
3	4	4
4	3	7
5	7	14
6	2	16
Total	16

Black: given data. Blue: working we add.

Add the frequencies to count all observations.

Middle position(s)

Use the two middle positions for an even total, and the single middle position for an odd total.

Median

Read the values at those positions, then average if there are two.

Question 2

Find the median.

Given information

Value	Frequency
4	5
5	3
6	8
7	2

Check answer

Locate the middle observation(s)

Value	Frequency	Cumulative frequency
4	5	5
5	3	8
6	8	16
7	2	18
Total	18

Black: given data. Blue: working we add.

Add the frequencies to count all observations.

Middle position(s)

Use the two middle positions for an even total, and the single middle position for an odd total.

Median

Read the values at those positions, then average if there are two.

Question 3

Find the median.

Given information

Value	Frequency
1	6
2	3
3	5
4	2

Check answer

Locate the middle observation(s)

Value	Frequency	Cumulative frequency
1	6	6
2	3	9
3	5	14
4	2	16
Total	16

Black: given data. Blue: working we add.

Add the frequencies to count all observations.

Middle position(s)

Use the two middle positions for an even total, and the single middle position for an odd total.

Median

Read the values at those positions, then average if there are two.

Question 4

Find the median.

Given information

Value	Frequency
2	2
3	4
4	6
5	2

Check answer

Locate the middle observation(s)

Value	Frequency	Cumulative frequency
2	2	2
3	4	6
4	6	12
5	2	14
Total	14

Black: given data. Blue: working we add.

Add the frequencies to count all observations.

Middle position(s)

Use the two middle positions for an even total, and the single middle position for an odd total.

Median

Read the values at those positions, then average if there are two.

Question 5

Find the median.

Given information

Value	Frequency
3	3
4	4
5	7
6	2

Check answer

Locate the middle observation(s)

Value	Frequency	Cumulative frequency
3	3	3
4	4	7
5	7	14
6	2	16
Total	16

Black: given data. Blue: working we add.

Add the frequencies to count all observations.

Middle position(s)

Use the two middle positions for an even total, and the single middle position for an odd total.

Median

Read the values at those positions, then average if there are two.