1. Measures of Central Tendency and Dispersion from Grouped Data
Lesson 3 - 3
Measures of Central Tendency and Dispersion from Grouped Data

2. Objectives Approximate the mean of a variable from grouped data
Compute the weighted mean
Approximate the variance and standard deviation of a variable from grouped data

3. Vocabulary
Weighted Mean – mean of a variable value times its weighted value

4. Calculating Stats from Summary Data
Each class is assumed to have all of its data at the class midpoint
Each classes observations serve as the weighted value
GPA example: ∑ class hours * class grade = GPA This is a weighted average!

5. Descriptive Stats from Summary Stats
Class
Midpt xi
Freq fi
xi fi
xi - x
(xi – x)²fi
0 – 1.99 1 2
-5.1
52.02
2 – 3.99 3 5 15
-3.1
48.05
4 – 5.99 6 30
-1.1
7.26
6 – 7.99 7 8 56
0.9
6.48
8 – 9.99 9 81
2.9
75.69
Total
Σfi = 30
Σxifi = 184
Σ(xi – x)²fi = 189.5
Mean
Variance
Σxifi = 184
x ≈ = 6.1
Σfi = 30
Σ(xi – x)² fi = 189.5
s² ≈ = 6.53
Σfi – 1 = 29

6. Descriptive Stats from Summary Stats
Class
Midpt xi
Freq fi
xi fi
xi - x
(xi – x)²fi
0 – 1.99 1 2
-5.1
52.02
2 – 3.99 3 5 15
-3.1
48.05
4 – 5.99 6 30
-1.1
7.26
6 – 7.99 7 8 56
0.9
6.48
8 – 9.99 9 81
2.9
75.69
Total
Σfi = 30
Σxifi = 184
Σ(xi – x)²fi = 189.5
n/2 – CF /2 - 13
Median = M ≈ L (ci) = (2) = 6 + (2/8) 2 = 6.25 f
L is the lower class limit of the class containing the median
n is the total number of data values in the frequency distribution
CF is the cum freq of the class preceding the median class
f is the frequency of the median class
ci is the class width of the median class

7. Summary & Homework Summary Homework: pg 161 - 165: 3, 4, 5, 21, 25
Use raw data whenever possible
If grouped (summarized data) is the only data available, estimates for mean and standard deviation can still be obtained using class midpoints and numbers in each class
Homework: pg : 3, 4, 5, 21, 25