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Mean from frequency table with discrete data
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The following gives the formula to find the mean of grouped data from a frequency table. Scroll down the page for more examples and solutions.
How to find the mean from a frequency distribution table?
The following example shows how to determine the
mean from a frequency table with intervals or grouped frequency table.
Example:
The following table shows the frequency distribution of the diameters of 40 bottles. (Lengths have been measured to the nearest millimeter) 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 
Midpoint (x) 
37 
42 
47 
52 
57 
Step 2: Multiply the frequency of each interval by its midpoint
Diameter (mm) 
35 – 39 
40 – 44 
45 – 49 
50 – 54 
55 – 60 
Frequency (f) 
6 
12 
15 
10 
7 
Midpoint (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 
Midpoint (x) 
37 
42 
47 
52 
57 

f × x 
222 
504 
705 
520 
399 
2350 
How to find the mean, mode and median from a frequency table for both discrete
and grouped data?
Mean: multiply midpoints by frequencies and add the subtotals. Divide by the total of the frequencies.
Mode: find the largest frequency  the corresponding value is the modal value or modal class.
Median: calculate a running total of the frequencies  the first interval that is above half the total contains the median.
How to find the mean from a frequency table for both discrete and grouped data?
How to get 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.
How to use a TI84 calculator to calculate the Mean and Standard Deviation of a Frequency Distribution?
Find the mean and the standard deviation of the population data summarized by the following frequency distribution.
How to use a TI84 calculator to calculate the Mean and Standard Deviation of a Grouped Frequency Distribution?
Find the mean and the standard deviation of the sample data summarized by the following frequency distribution.
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