Posted by Anjali Kaur on May 05, 2021

Discrete Series Arithmetic Mean

Discrete series is the second type of series. Discrete series is also known as the ungrouped frequency distribution. Under this series, we have X and F, where F is the frequency, that is, the number of times X is repeated. There are 3 methods involved under the discrete series arithmetic mean calculation. Let’s understand each method.

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1. Direct Method

This is the most simple method of all, its formula is:

Steps involved:

1. Find FX, just multiply the X values with F values. Then add them up, to get ΣFX.
2. Find ΣF
3. Apply the formula; x̄ = ΣFX/ΣF

Let’s try a question; if X and F is given in the question.

X	F	XF
10	2	20
30	3	90
20	4	80
40	1	40
Σ	10	230

Using the arithmetic mean formula, x̄ = ΣFX/ΣF

x̄ = 230/10 = 23

2. Short-cut Method

This method is also known as the assumed mean method. It’s formula is

Steps involved:

1. Take assume mean, A, from X, generally I recommend selecting the middle term.
2. Find d, which is the deviation from the assumed means. Use d= X-A.
3. Find Fd, which is frequency multiply with deviation, d. Then find the summation of the same.
4. Find the total frequency. Then use the above formula. x̄ = A + ΣFd/ΣF

Let’s try a question.

X	F	d= X-A	Fd
10	2	-20	-40
30*A	3	0	0
20	4	-10	-40
40	1	10	10
Σ	10		-70

Now, use the formula;

x̄ = A + ΣFd/ΣF

= 30 -70/10

=23

3. Step-Deviation method

Since the name of the method says step deviation, we try to do the calculation faster by taking out a common factor from X. Look at the formula:

Steps involved:

1. Find assume mean, A, from X. Try selecting the middle term.
2. Find d, which is d= X-A
3. Find d’, which is d’ = X-A/C; C is the common factor, just like an LCM taken from X.
4. Find Fd’ and take the total of it. Then use the formula; x̄ = A + ΣFd’/ΣF x C

Let’s try a question.

X	F	d= X-A	d’ = X-A/C ; C = 10	Fd’
10	2	-20	-2	-4
30*A	3	0	0	0
20	4	-10	-1	-4
40	1	10	1	1
Σ	10			-7

Use the formula;

x̄ = A + ΣFd’/ΣF x C

= 30 -7/10 x10

= 23

Take a look at my video explanation:

Test Yourself

1. From the following data of the marks obtained by 60 students of a class, calculate the average marks by the direct method, assume mean method, and step – deviation method.

Marks	No of students
20	8
30	12
40	20
50	10
60	6
70	4

2. From the following data, calculate arithmetic mean by direct method, short-cut method and step-deviation method.

X	F
2	10
3	16
4	11
5	8
6	6
7	4
8	3
9	2

3. Calculate average of the following discrete series. Use Assumed mean method by taking 25 as assumed mean.

Size	Frequency
30	2
29	4
28	5
27	3
26	2
25	7
24	1
23	4
22	5
21	7

4. Marks secured by 42 students in economics are as follows, find the average marks.

Marks	Number of Students
15	8
20	4
22	7
23	3
27	8
35	7
18	5

This was all about discrete series arithmetic mean.

I hope it was helpful, you can refer more posts related to the statistics.

1. Individual Series Arithmetic Mean
2. Introduction to the statistics.
3. Functions and importance of statistics.

Thank You!

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