This document provides steps for calculating the median of grouped data:
1. Create a frequency distribution table with class intervals, frequencies, and cumulative frequencies.
2. Find the median class by calculating N/2, where N is the total number of data points.
3. The median is calculated using the formula: x = L + (n2 - F2)/f2 * i, where L is the lower limit of the median class, n2 is the median class, F2 is the cumulative frequency before the median class, f2 is the frequency of the median class, and i is the class interval.
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Taking of a measurement and the process of counting yield numbers that contain information. The objective of a person applying the tools of statistics to these numbers is to determine the nature of this information.
This task is made much easier if the numbers are organized and summarized.
Even quite small data sets are difficult to understand without some summarization. Statistical quantities such as the mean and variance can be extremely helpful in summarizing data but first we discuss tabular and graphical summaries.
There are several ways to present a statistical data like;
Frequency table
Simple bar diagrams
Multiple Bar Diagrams
Histogram
Frequency Polygon etc.
Steam and Leaf plots
Pie Charts
A frequency distribution is a tabular arrangement of data in which various items are arranged into classes or groups and the number of items falling in each class is stated.
The number of observations falling in a particular class is referred to as class frequency and is denoted by "f".
In frequency distribution all the values falling in a class are assumed to be equal to the midpoint of that class.
Data presented in the form of a frequency distribution is also called grouped data. A frequency distribution table contains a condensed summary of the original data.
There are two types of frequency distribution i) Simple Frequency distribution ) ii) Grouped Frequency distribution.
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3. Steps in calculating Median of grouped data
• Make the frequency distribution table.
• Make a column for the less than cumulative frequency (<cf)
• Find for the median class using 𝑚𝑑 𝑐𝑙𝑎𝑠𝑠 =
𝑁
2
• Locate the median class in your table by looking at the
cumulative frequency where it lies, then put markings in the
class.
• Calculate the median from grouped data:
𝑥 = 𝐿 +
𝑛
2
− 𝐹2
𝑓2
𝑖
Where: L=exact lower limit of the interval where the median lies
𝑛
2
= 𝑚𝑒𝑑𝑖𝑎𝑛 𝑐𝑙𝑎𝑠𝑠; i=class interval; 𝑓2=frequency of median class
𝐹2=cumulative frequency up to the class immediately preceding the median class
5. Make the frequency distribution table.
Class interval tally frequency
84 – 86 2
81 – 83 4
78 – 80 3
75 – 77 5
72 – 74 5
69 – 71 4
66 – 68 3
63 - 65 3
60 -62 1
N = 30
6. Make a column for the less than cumulative frequency (<cf)
Class
interval
f <cf
84 – 86 2 30
81 – 83 4 28
78 – 80 3 24
75 – 77 5 21
72 – 74 5 16
69 – 71 4 11
66 – 68 3 7
63 - 65 3 4
60 -62 1 1
N = 30
To find the cumulative frequency start
at the bottom by copying the
frequency in the lowest class interval.
Then to get the next cumulative
frequency simply add the preceding
frequency.
1 + 3 = 4
4 + 3 = 7
7 + 4 = 11
7. Find for the median class using 𝑚𝑑 𝑐𝑙𝑎𝑠𝑠 =
𝑁
2
Class
interval
f <cf
84 – 86 2 30
81 – 83 4 28
78 – 80 3 24
75 – 77 5 21
72 – 74 5 16
69 – 71 4 11
66 – 68 3 7
63 - 65 3 4
60 -62 1 1
N = 30
𝑚𝑑 𝑐𝑙𝑎𝑠𝑠 =
𝑁
2
𝑚𝑑 𝑐𝑙𝑎𝑠𝑠 =
30
2
𝒎𝒅 𝒄𝒍𝒂𝒔𝒔 = 𝟏𝟓
8. Locate the median class in your table by looking at the cumulative
frequency where it lies, then put markings in the class.
Class
interval
f <cf
84 – 86 2 30
81 – 83 4 28
78 – 80 3 24
75 – 77 5 21
72 – 74 5 16
69 – 71 4 11
66 – 68 3 7
63 - 65 3 4
60 -62 1 1
N = 30
𝒎𝒅 𝒄𝒍𝒂𝒔𝒔 = 𝟏𝟓
Note: when the computed
md class is not present in the
<cf column, choose the
number higher than but
nearer the computed md class.
In this case the computed md
class which is 15 is not present
In the <cf column, so we will
choose the number higher to
It which is 16.
Put markings in the class where
It lies.
9. Calculate the median from grouped data.
Class
interval
f <cf
84 – 86 2 30
81 – 83 4 28
78 – 80 3 24
75 – 77 5 21
72 – 74 5 16
69 – 71 4 11
66 – 68 3 7
63 - 65 3 4
60 -62 1 1
N = 30
𝑥 = 𝐿 +
𝑛
2
− 𝐹2
𝑓2
𝑖
Where: L=exact lower limit of the class
interval where the median class lies
𝑛
2
= 𝑚𝑒𝑑𝑖𝑎𝑛 𝑐𝑙𝑎𝑠𝑠; i=class interval;
𝑓2=frequency of median class
𝐹2=cumulative frequency up to the
class immediately preceding the
median class
L = LS of the md class – 0.5
L = 72 – 0.5
L = 71.5
10. Calculate the median from grouped data.
Class
interval
f <cf
84 – 86 2 30
81 – 83 4 28
78 – 80 3 24
75 – 77 5 21
72 – 74 5 16
69 – 71 4 11
66 – 68 3 7
63 - 65 3 4
60 -62 1 1
N = 30
𝑥 = 𝐿 +
𝑛
2
− 𝐹2
𝑓2
𝑖
Where: L=exact lower limit of the class
interval where the median class lies
𝑛
2
= 𝑚𝑒𝑑𝑖𝑎𝑛 𝑐𝑙𝑎𝑠𝑠; i=class interval;
𝑓2=frequency of median class
𝐹2=cumulative frequency up to the
class immediately preceding the
median class
L = 71.5
𝑛
2
= 15
𝑖 = 3
𝐹2 = 11
𝑓2 = 5
11. Calculate the median from grouped data.
Class
interval
f <cf
84 – 86 2 30
81 – 83 4 28
78 – 80 3 24
75 – 77 5 21
72 – 74 5 16
69 – 71 4 11
66 – 68 3 7
63 - 65 3 4
60 -62 1 1
N = 30
𝑥 = 𝐿 +
𝑛
2
− 𝐹2
𝑓2
𝑖
L = 71.5 𝐹2 = 11 𝑖 = 3
𝑛
2
= 15 𝑓2 = 5
𝑥 = 71.5 +
15 − 11
5
3
𝑥 =73.9
Note: The median must be in two
decimal places only. And also the
answer in the median must lies in the
median class.