Mean from Frequency Tables with Intervals

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

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

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