1. Check Homework, Ask ?s

2. Objective
3-3
Today we learn mean, median, and mode for grouped and ungrouped frequency distributions.
Summarize data using the measures of central tendency, such as the mean, median, mode, and midrange. 3

3. 3-2 The Sample Mean for an Ungrouped Frequency Distribution
3-13 13

4. 3-2 The Sample Mean for an Ungrouped Frequency Distribution - Example
3-14
Score, X
Frequency, f
Score, X
Frequency, f 2 2 1 4 1 4 2 12 2 12 3 4 3 4 4 3 4 3 5 5 14

5. 3-2 The Sample Mean for an Ungrouped Frequency Distribution - Example
3-15
1) Create a new column
(f times x)
Score, X
Frequency, f f × X 2 1 4 12 24 3
Score, X
Frequency, f × f X 2 1 4 4 2 12 24
2) Find the sum of your new column (Σf∙X = 52) 3 4 12 4 3 12 5 5
3) Use the mean formula 15

6. 3-2 The Sample Mean for a Grouped Frequency Distribution
3-16
The
mean
for a
grouped
frequency
distributu
ion is
given by X f n
Here
the
correspond
ing
class
midpoint. m = ( ) × å . 16

7. 3-2 The Sample Mean for a Grouped Frequency Distribution - Example
3-17
Create a new column for the midpoint of each group
Class
Frequency, f
Class
Frequency, f 3 3 5 5 4 4 3 3 2 2 5 5 17

8. 3-2 The Sample Mean for a Grouped Frequency Distribution - Example
3-18
Midpoint of each class
Frequency times Midpoint
Class
Frequency, f X m f × 3 18 54 5 23
115 4 28
112 33 99
Class
Frequency, f X × f X m m 3 18 54 5 23
115 4 28
112 3 33 99 2 38 76
Sum of this column is 17 (n = 17)
Sum of this column is 456 2 38 76 5 5 18

9. 3-2 The Sample Mean for a Grouped Frequency Distribution - Example
3-19 19

10. 3-2 The Median-Ungrouped Frequency Distribution
3-28
For an ungrouped frequency distribution, find the median by examining the cumulative frequencies to locate the middle value. 28

11. 3-2 The Median-Ungrouped Frequency Distribution
3-29
If n is the sample size, compute n/2. Locate the data point where n/2 values fall below and n/2 values fall above.
In other words, add up your frequencies and divide by 2 29

12. 3-2 The Median-Ungrouped Frequency Distribution - Example
3-30
LRJ Appliance recorded the number of VCRs sold per week over a one-year period. The data is given below.
No. Sets Sold
Frequency 1 4 2 9 3 6 5 30

13. 3-2 The Median-Ungrouped Frequency Distribution - Example
3-31
No. Sets Sold
Frequency 1 4 2 9 3 6 5
To locate the middle point, divide n by 2; 24/2 = 12.
Locate the point where 12 values would fall below and 12 values will fall above.
Consider the cumulative distribution.
The 12th and 13th values fall in class 2. Hence MD = 2.
n = 24 31

14. 3-2 The Median-Ungrouped Frequency Distribution - Example
3-32
This class contains the 5th through the 13th values. 32

15. 3-2 The Median for a Grouped Frequency Distribution
3-33
class
median
the of
boundary
lower L
width w
frequency f
preceding
immediately
cumulative cf
frequencies
sum n
Where MD
can be computed from:
The m = ) ( 2 + -
Keep this written somewhere handy 33

16. 3-2 The Median for a Grouped Frequency Distribution - Example
3-34
Class
Frequency, f
Class
Frequency, f 3 3 5 5 4 4 3 3 2 2 5 5 34

17. 3-2 The Median for a Grouped Frequency Distribution - Example
3-35 f
Class
Frequency, f
Cumulative
Frequency 3 5 8 4 12 15 2 17
Class
Frequency, f
Cumulative cf
Median Class
Frequency 3 3 Lm 5 8 4 12
w = = 5 3 15 2 17
n=17 so MD is 17/2 or 8.5 5 5 35

18. 3-2 The Median for a Grouped Frequency Distribution
3-37 n = 17 cf = 8 f = 4 w =
25.5 –
20.5 = 5 L = 25 . 5 m ( n 2 ) - cf
(17 / 2) – 8 MD = ( w ) + L = ( 5 ) + 25 . 5 f m 4 = 37

19. 3-2 The Mode for an Ungrouped Frequency Distribution - Example
3-42
Values
Frequency, f
Values
Frequency, f 15 3
Mode 15 3 20 5 20 5 25 8 25 8 30 3 30
So the mode is half of that, or 10.5
Σf = 21 3 35 2 35 2 5 5 42

20. 3-2 The Mode for a Grouped Frequency Distribution - Example
3-44
Modal
Class
So the mode is half of that, or 10
Σf = 20 44