Estimating the mean from grouped data Revision Card

AI generatedStatisticsKey Stage 3

Estimating the mean from grouped data.

Add a midpoint column: midpoint = (lower boundary + upper boundary) ÷ 2.
Multiply each midpoint by its frequency, then add the products and frequencies separately.
Estimated mean = Σmf ÷ Σf. Use each class’s own midpoint, especially when widths differ.

Example 1

Estimate the mean to 2 d.. The class widths are equal.

Given information

Class	Frequency
	3
	5
	7
	2

Add midpoint and product columns

-Class
 .5
 .5
 .5
-.5
-Total
+.5

Black: given data. Blue: working we add.

Find each midpoint from its own class boundaries.

Multiply each midpoint by its frequency, then total the

and mf columns.

Estimated mean

Use Σmf ÷ Σf. Unequal widths still use their own midpoint; do not use frequency density.

Estimated mean

Round at the end. It is an estimate because the exact values within each class are unknown.

Example 2

Estimate the mean to 2 d.. The class widths are unequal.

Given information

Class	Frequency
	4
	5
	8
	2

Add midpoint and product columns

Class		Midpoint
	4	5	20
	5	17.5	87.5
	8	32.5	260
	2	50	100
Total	19		467.5

Black: given data. Blue: working we add.

Find each midpoint from its own class boundaries.

Multiply each midpoint by its frequency, then total the

and mf columns.

Estimated mean

Use Σmf ÷ Σf. Unequal widths still use their own midpoint; do not use frequency density.

Estimated mean

Round at the end. It is an estimate because the exact values within each class are unknown.

Your turn

Question 1

Estimate the mean to 2 d.. The class widths are equal.

Given information

Class	Frequency
	5
	5
	9
	2

Check answer

Add midpoint and product columns

-Class
 .5
 .5
 .5
-.5
-Total
+.5

Black: given data. Blue: working we add.

Find each midpoint from its own class boundaries.

Multiply each midpoint by its frequency, then total the

and mf columns.

Estimated mean

Use Σmf ÷ Σf. Unequal widths still use their own midpoint; do not use frequency density.

Estimated mean

Round at the end. It is an estimate because the exact values within each class are unknown.

Question 2

Estimate the mean to 2 d.. The class widths are unequal.

Given information

Class	Frequency
	6
	5
	10
	2

Check answer

Add midpoint and product columns

Class		Midpoint
	6	5	30
	5	17.5	87.5
	10	32.5	325
	2	50	100
Total	23		542.5

Black: given data. Blue: working we add.

Find each midpoint from its own class boundaries.

Multiply each midpoint by its frequency, then total the

and mf columns.

Estimated mean

Use Σmf ÷ Σf. Unequal widths still use their own midpoint; do not use frequency density.

Estimated mean

Round at the end. It is an estimate because the exact values within each class are unknown.

Question 3

Estimate the mean to 2 d.. The class widths are equal.

Given information

Class	Frequency
	7
	5
	7
	2

Check answer

Add midpoint and product columns

-Class
 .5
 .5
 .5
-.5
-Total
+.5

Black: given data. Blue: working we add.

Find each midpoint from its own class boundaries.

Multiply each midpoint by its frequency, then total the

and mf columns.

Estimated mean

Use Σmf ÷ Σf. Unequal widths still use their own midpoint; do not use frequency density.

Estimated mean

Round at the end. It is an estimate because the exact values within each class are unknown.

Question 4

Estimate the mean to 2 d.. The class widths are unequal.

Given information

Class	Frequency
	3
	6
	8
	2

Check answer

Add midpoint and product columns

Class		Midpoint
	3	5	15
	6	17.5	105
	8	32.5	260
	2	50	100
Total	19		480

Black: given data. Blue: working we add.

Find each midpoint from its own class boundaries.

Multiply each midpoint by its frequency, then total the

and mf columns.

Estimated mean

Use Σmf ÷ Σf. Unequal widths still use their own midpoint; do not use frequency density.

Estimated mean

Round at the end. It is an estimate because the exact values within each class are unknown.

Question 5

Estimate the mean to 2 d.. The class widths are equal.

Given information

Class	Frequency
	4
	6
	9
	2

Check answer

Add midpoint and product columns

Class		Midpoint
	4	3	12
	6	9	54
	9	15	135
	2	21	42
Total	21		243

Black: given data. Blue: working we add.

Find each midpoint from its own class boundaries.

Multiply each midpoint by its frequency, then total the

and mf columns.

Estimated mean

Use Σmf ÷ Σf. Unequal widths still use their own midpoint; do not use frequency density.

Estimated mean

Round at the end. It is an estimate because the exact values within each class are unknown.