This document defines and explains measures of central tendency (mean, median, mode) and measures of variability (range, standard deviation, variance) for both ungrouped and grouped data. It provides examples of calculating the mean, median, mode, range, and standard deviation for a data set with values grouped into classes. Standard deviation and variance measure how spread out numbers are from the average (mean) and are calculated using the formula provided.

1. MEASURES OF
CENTRAL TENDENCY
MEAN, MEDIAN, AND MODE

2. MEAN
UNGROUPED DATA GROUPED DATA

3. MEAN (GROUPED DATA)

4. CLASS FREQUENCY
(f)
CLASS
MARK
fX
12-17 5
18-23 6
24-29 8
30-35 12
36-41 10
42-47 5
48-53 4
i=6 n=50 𝑓𝑋 =

7. WEIGHTED MEAN

8. MEDIAN
UNGROUPED DATA GROUPED DATA
middle entry/term

10. CLASS FREQUENCY
(f)
CLASS
MARK
fX <cf
12-17 5 14.5 72.5
18-23 6 20.5 123
24-29 8 26.5 212
30-35 12 32.5 390
36-41 10 38.5 385
42-47 5 44.5 222.5
48-53 4 50.5 202
i=6 n=50 𝑓𝑋 =1395

12. MODE
UNGROUPED DATA GROUPED DATA
most frequently occurred
in a set of data

13. CLASS FREQUENCY
(f)
CLASS
MARK
fX
12-17 5
18-23 6
24-29 8
30-35 12
36-41 10
42-47 5
48-53 4
i=6 n=50 𝑓𝑋 =

15. MEASURES OF
VARIABILITY
RANGE, STANDARD DEVIATION, AND VARIANCE

16. RANGE
UNGROUPED DATA GROUPED DATA
R=H-L R=UCB-LCB

17. CLASS FREQUENCY
(f)
CLASS
MARK
fX
12-17 5
18-23 6
24-29 8
30-35 12
36-41 10
42-47 5
48-53 4
i=6 n=50 𝑓𝑋 =

18. INTERQUARTILE RANGE
the middle half of the data
11,13,16,19,20,21,23,25,26,29,
33,34,36,38,39,46,52,55,58

19. STANDARD DEVIATION
UNGROUPED DATA GROUPED DATA

21. CLASS FREQUENCY
(f)
CLASS
MARK
fX X-𝒙 (X−𝒙)2 f(X−𝒙)2
12-17 5 14.5 72.5 7.36
18-23 6 20.5 123 13.36
24-29 8 26.5 212 19.36
30-35 12 32.5 390 25.36
36-41 10 38.5 385 31.36
42-47 5 44.5 222.5 37.36
48-53 4 50.5 202 43.36
i=6 n=50 𝑓𝑋 =1607 f(X−𝒙)2
=

22. VARIANCE
UNGROUPED DATA GROUPED DATA