This document discusses measures of central tendency - mean, median, and mode - for grouped data. It provides examples of calculating the mean, median, and mode using frequency distributions with class intervals and frequencies. The mean is calculated using the class midpoint formula or coded formula. The median is found by determining the median class based on the cumulative frequency. The mode is the class with the highest frequency.

1. Measures of Central Tendency
Mean, Median and Mode
for Grouped Data
Basic Statistics

2. Mean for Grouped Data
Xam

3. Classmark Formula
The following IQ frequency distribution was obtained from 100
randomly selected high school students. Solve the mean.
Class Interval f Xm fXm
90 – 98 6 564
94
99 – 107 22 103 2266
108 – 116 40 112 4480
117 – 125 24 121 2904
126 – 134 8 130 1040
N = 100 =11254

4. Your turn!
The following data represent the scores(in words per minute) of 47
computer encoders on a speed test.
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
MEAN: ________________

5. Coded Formula
The following IQ frequency distribution was obtained from 100
randomly selected high school students. Solve the mean.
Class Interval f d fd
90 – 98 6 -2 - 12
99 – 107 22 -1 - 22
108 – 116 40 0 0
117 – 125 24 1 24
126 – 134 8 2 16
N = 100 =6

6. Your turn!
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.
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
MEAN: ________________

7. Median for Grouped Data

8. Computing the Median of Grouped Data
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
Class Interval f <cf than cumulative
frequency.
90 – 98 6 6
2. Determine the median
99 – 107 22 28 class. This is the class
108 – 116 40 68 interval containing half of the
total frequency in the <cf
117 – 125 24 92 column.
126 – 134 8 100 3. Use the formula to
find the median.
N = 100

9. Your turn!
The following data represent the scores(in words per minute) of 47
computer encoders on a speed test.
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
MEDIAN: ________________

10. Mode for Grouped Data

11. Mode for Grouped Data
The following is an illustration on finding the mode of the IQ
frequency distribution obtained from 100 randomly selected high
school students.
Class Interval f
1. Find the mode class.
90 – 98 6 This is the class with the
highest frequency.
99 – 107 22
108 – 116 40
2. Use the formula
117 – 125 24 to find the mode.
126 – 134 8
N = 100
= 112.26

12. Mode for Grouped Data

13. Your turn!
The following data represent the scores(in words per minute) of 47
computer encoders on a speed test. Compute the mode .
Class Interval f
55 – 60 2
61 – 66 5
67 – 72 8
73 – 78 10
79 – 84 9
85 – 90 8
91 - 96 5
MODE: ________________