Question

Find the arithmetic mean of the following date (correct to the nearest whole number) using the step-deviation method.

x	5	10	15	20	25	30	35	40	45	50
y	20	43	75	67	72	45	39	9	8	6

Answer 1

Hint: In the step deviation method, we take an assumed mean from the frequencies, and by using the formula of step deviation method, we can find the arithmetic mean. The values which are given here as y are the frequencies. They have also asked it to correct to the nearest whole number.

Complete step by step answer:
We know that the formula used to find the arithmetic mean for a data using step deviation is
$\bar x\, = A + \dfrac{{\sum d }}{N}$
where A is assumed mean,
 and d is (y-A) according to the above question,
and N is the sum of all x
Let us assume that the assumed mean is 40
which implies A= 40.
which implies the table will be

x	y	(y-A)	d
5	20	20-40	-20
10	43	43-40	3
15	75	75-40	35
20	67	67-40	27
25	72	72-40	32
30	45	45-40	5
35	39	39-40	-1
40	9	9-40	-31
45	8	8-40	-32
50	6	6-40	-34
			-16
			∑d

From the above table we can say that N = (5+10+15+20+25+30+35+40+45+50) = 275
which implies $\bar x$= 40+(-16/275) = 39.947
It is given that we should correct the answer to the nearest whole number so the mean will be 40.

Note:
Learn all the formulae of all the methods to find mean, median, mode and all the information. Do not make calculation mistakes while solving these type of questions. you can also try this problem by direct method but not all problems can be solved by direct so use this method mostly. Read the question properly.