STATISTICS

1. MEAN, MEDIAN AND
MODE OF GROUPED DATA

2. MEAN
𝒙 =
𝒇𝒙𝒎
𝒏
where:
X = measurement or score
f = frequency
xm = class mark
n = total frequency

3. MEDIAN
𝑿 = 𝑥𝐿𝐵 +
𝑛
𝟐
−<𝐶𝑓
𝑓𝑚
i
where:
X LB= lower class boundary of the median class
f = total frequency
<cf = less than cumulative frequency above the median class
i= size of class interval
fm = frequency of the median class

4. MODE
𝐱 = 𝑥𝐿𝐵 +
𝑑1
𝑑1+𝑑2
i
where:
X LB= lower class boundary of the modal class
𝑑1 = difference between the frequency in the modal class and
frequency in the preceding class interval
𝑑𝟐 = difference between the frequency in the modal class and
frequency in the succeeding class interval
i= size of the class interval

5. EXAMPLE 1 Below is a frequency distribution of scores of 30 students in mathematics. Compute for the
mean, median and mode
Class Interval frequency (f) Class Mark(xm) fXm
cumulative
frequency (<cf)
6-10 1 8 8 1
11-15 1 13 13 2
16-20 2 18 36 4
21-25 2 23 46 6
26-30 3 28 84 9
31-35 6 33 198 15
36-40 7 38 266 22
41-45 4 43 172 26
46-50 2 48 96 28
51-55 1 53 53 29
56-60 1 58 58 30

6. 𝒙 = 34.33
The scores in
Mathematics are
a little bit higher
and lower than
34.33
𝑿 = 35.5
50% of the
students got a
score lower than
35
𝐱 = 37.16
Class interval
36-40 is the class
mode with the
highest
frequency equal
to 7.

7. EXAMPLE 2 The table below shows the age distribution of the contestants in a raffle draw sponsored by a
popular noontime gameshow. Compute for the mean, median and mode
Class Interval frequency (f) Class Mark(xm) fXm
cumulative
frequency (<cf)
7-9 1 8 8 1
10-12 1 11 11 2
13-15 4 14 56 6
16-18 6 17 102 12
19-21 14 20 280 26
22-24 10 23 230 36
25-27 3 26 78 39
28-30 1 29 29 40

8. 𝒙 = 19.85
The age of the
contestants are a
little bit higher
and lower than
19.85
𝑿 = 20.21
50% of the 40
contestants got
an age lower than
20.21
𝐱 = 20.5
Class interval
19-20 is the class
mode with the
highest
frequency equal
to 14.

9. ASSIGNMENT Below is the frequency distribution table of the test scores in Chemistry. Complete the table and
compute for the mean, median and mode.
Class Interval frequency (f) Class Mark(xm) fXm
cumulative
frequency (<cf)
45-49 1
50-54 9
55-59 3
60-64 17
65-69 15
70-74 2
75-79 3