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Mean from Frequency Tables with Intervals




The following example shows how to determine the mean from a frequency table with intervals or grouped frequency table.

Related Topics:
Mean from frequency table with discrete data

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Example:

The following table shows the frequency distribution of the diameters of 40 bottles. (Lengths have been measured to the nearest millimetre) Find the mean of the data.

Diameter (mm)

35 – 39

40 – 44

45 – 49

50 – 54

55 – 60

Frequency

6

12

15

10

7

Solution:

Step 1: Find the midpoint of each interval.

Midpoint of interval = (Lower class limit + Upper class limit)

= (39 + 35) = 37

Diameter (mm)

35 – 39

40 – 44

45 – 49

50 – 54

55 – 60

Frequency (f)

6

12

15

10

7

Mid-point (x)

37

42

47

52

57

Step 2: Multiply the frequency of each interval by its mid-point

Diameter (mm)

35 – 39

40 – 44

45 – 49

50 – 54

55 – 60

Frequency (f)

6

12

15

10

7

Mid-point (x)

37

42

47

52

57

f × x

222

504

705

520

399

Step 3: Get the sum of all the frequencies (f) and the sum of all the fx. Divide ‘sum of fx’ by ‘sum of f ’ to get the mean.

Total

Diameter (mm)

35 – 39

40 – 44

45 – 49

50 – 54

55 – 60

Frequency (f)

6

12

15

10

7

50

Mid-point (x)

37

42

47

52

57

f × x

222

504

705

520

399

2350



 

The following video shows how to find the mean, mode and median from a frequency table for both discrete and grouped data.



The following video shows how to find the mean from a frequency table for both discrete and grouped data.




 

Getting averages from grouped frequency tables, including the range, mean, median and mode.


How to work out the mean from a grouped frequency table. First work out the midpoints of each group. Then multiply the midpoints by the frequency. Divide the total of this column by the total frequency.




 

You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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