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.







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