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### Finding Weighted Means and Averages For Frequency Distributions

posted Jan 31, 2014, 1:51 PM by Prof Kiernan   [ updated Feb 5, 2014, 5:58 PM ]
Find the mean of this frequency distribution:

 class frequency 10-19 8 20-29 16 30-39 21 40-49 11 50-59 4

1. The first thing you need to do is to find the midpoint for each class.
 Class Midpoint 10-19 (10+19)/2 = 14.5 20-29 (20+29)/2 = 24.5 30-39 (30+39)/2 = 34.5 40-49 (40+49)/2 = 44.5 50-59 (50+59)/2 = 54.5

2. Next multiply each midpoint by the corresponding frequency and get the total.
 Midpoint Frequency Midpoint * frequency 14.5 8 14.5 * 8 =    116 24.5 16 24.5 * 16 =    392 34.5 21 34.5 * 21 = 724.5 44.5 11 44.5 * 11 = 489.5 54.5 4 54.5 * 4 =    218 Total: 60 Total: 1940

3. Finally divide the total of the Midpoint * frequency column by the total of the frequency column to get your mean.
1940 / 60 = 32.333333333...
Always round to one value beyond what your original data was (since our classes were whole numbers we should round to 1 decimal place). So our final answer for the mean of this frequency distribution is 32.3.