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Measures of Central Tendency
Mean, Median and Modefor Grouped Data
Basic Statistics
Mean for Grouped Data
Classmark Formula
where X = class mark f = frequency n = number of sample
Coded Formula
where Xam = assumed mean f = frequency
d = coded deviation i = class size
Classmark Formula
Class Interval f Xm fXm
90 – 98 6
99 – 107 22
108 – 116 40
117 – 125 24
126 – 134 8
N = 100
94
103
112
121
130
564
4480
2904
1040
2266
=11254
The following IQ frequency distribution was obtained from 100 randomly selected high school students. Solve the mean.
Your turn!
Class Interval f Xm fXm
55 – 60 2
61 – 66 5
67 – 72 8
73 – 78 10
79 – 84 9
85 – 90 8
91 - 96 5
The following data represent the scores(in words per minute) of 47 computer encoders on a speed test.
MEAN: ________________
Coded Formula
Class Interval f d fd
90 – 98 6
99 – 107 22
108 – 116 40
117 – 125 24
126 – 134 8
N = 100
-2
-1
0
1
2
- 12
0
24
16
- 22
= 6
The following IQ frequency distribution was obtained from 100 randomly selected high school students. Solve the mean.
¿112+( 6100 )9
Your turn!
Class Interval f d fd
55 – 60 2
61 – 66 5
67 – 72 8
73 – 78 10
79 – 84 9
85 – 90 8
91 - 96 5
The following data represent the scores(in words per minute) of 47 computer encoders on a speed test. Compute the mean using the Coded formula.
MEAN: ________________
Median for Grouped Data
where = median l = lower class boundary of the median class n = number of sample
<cf = less than cumulative frequency above the median class
i = size of the class interval = frequency of the median class
~𝑋=𝑙+( 𝑛2 −<𝑐𝑓
𝑓 𝑚 )𝑖
Computing the Median of Grouped Data
Class Interval f <cf
90 – 98 6
99 – 107 22
108 – 116 40
117 – 125 24
126 – 134 8
N = 100
6
28
68
92
100
Let us illustrate the computation of the Median of Grouped Data using the IQ frequency distribution obtained from 100 randomly selected high school students.
1. Construct the less than cumulative frequency.
2. Determine the median class. This is the class interval containing half of the total frequency in the <cf column.
3. Use the formula to find the median.
~𝑋=𝑙+( 𝑛2 −<𝑐𝑓
𝑓 𝑚 )𝑖 9
¿112.45
Your turn!
Class Interval f <cf
55 – 60 2
61 – 66 5
67 – 72 8
73 – 78 10
79 – 84 9
85 – 90 8
91 - 96 5
The following data represent the scores(in words per minute) of 47 computer encoders on a speed test.
MEDIAN: ________________
Mode for Grouped Data
where = mode l = lower class boundary of the mode class = frequency of the mode class
= frequency above the mode class = frequency below the mode class
𝑀𝑜=𝑙+( 𝑓 𝑚− 𝑓 𝑎
2 𝑓 𝑚− 𝑓 𝑎− 𝑓 𝑏)𝑖
Mode for Grouped Data
Class Interval f
90 – 98 6
99 – 107 22
108 – 116 40
117 – 125 24
126 – 134 8
N = 100
The following is an illustration on finding the mode of the IQ frequency distribution obtained from 100 randomly selected high school students.
1. Find the mode class. This is the class with the highest frequency.
2. Use the formula to find the mode.
𝑀𝑜=𝑙+( 𝑓 𝑚− 𝑓 𝑎
2 𝑓 𝑚− 𝑓 𝑎− 𝑓 𝑏)𝑖 ¿107.5+( 40−22
2 (40 )−22−24 )9= 112.26
Mode for Grouped Data
The value of the mode may also be approximately determined by this relationship.
Example:
Using the same FDT,
Your turn!
Class Interval f
55 – 60 2
61 – 66 5
67 – 72 8
73 – 78 10
79 – 84 9
85 – 90 8
91 - 96 5
The following data represent the scores(in words per minute) of 47 computer encoders on a speed test. Compute the mode .
MODE: ________________
