1. Chapter 3: Averages and Variation
Section 3: Mean and Standard Deviation of Grouped Data

2. Sample mean for a frequency distribution
x = midpoint of class
f = frequency
n =

3. Sample standard deviation for a frequency distribution
x = midpoint of class
f = frequency
n =

4. Example
Class f
Midpoint (x)
0 – 2 4 1 -
9.2
84.64
338.56
3 – 5 3 12
-6.2
38.44
115.32
6 – 8 8 7 56
-3.2
10.24
81.92
9 – 11 15 10
150
-0.2
0.04
0.60
12 – 14 13
169
2.8
7.84
101.92
15 – 17 5 16 80
5.8
33.64
168.2
18 – 20 2 19 38
8.8
77.44
154.88 50
509
961.40

5. Example (Cont)