Lesson 3 - 3

1. 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 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 n/2 – CF 30/2 - 13 Median = M ≈ L + ------------ (ci) = 6 + ------------- (2) = 6 + (2/8) 2 = 6.25 f 8 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 • 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 161 - 165: 3, 4, 5, 21, 25