m and s for Grouped Data
Calculating the Mean from a Frequency Distribution
Since calculating the mean and standard deviation is tedious, we can save some of this work when we have a frequency distribution. Suppose we were interested in how many siblings are in statistics students' families. We come up with a frequency distribution table below.
Notice that since there are 29 respondents, calculating the mean would be very tedious. Instead, we see that there are five ones, 12 twos, 8 threes, 3 fours, and 1 seven. Hence the total count of siblings is
1(5) + 2(12) + 3(8) + 4(3) + 7(1) = 72
Now divide by the number of respondents to get the mean.
Extending the Frequency Distribution Table
Just as with the mean formula, there is an easier way to compute the standard deviation given a frequency distribution table. We extend the table as follows:
Next we calculate
Now finally apply the formula
Click here for an applet that finds statistics from grouped data.
Sometimes instead of the simple mean, we want to weight certain outcomes higher then others. For example, for your statistics class, the following percentages are given
Homework = 150
Midterm = 450
Project = 100
Final = 300
Suppose that you received an 88% on your homework, a 97% on your midterms, a 98% on your project and an 78% on your final. What is your average for you class?
To compute the weighted average, we use the formula
Sxw = .88(150) + .97(450) + .98(100) + .78(300) = 900.5
Sw = 150 + 450 + 100 + 300 = 1000
Now divide to get your weighted average
You squeaked by with an "A".