Find mean by direct method,assumed mean method and step deviation method if CI are 0-10,10-20,20-30,30-40,40-50 and fi are 7,10,15,8,10.?

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Answer

DIRECT METHOD= 25.8,ASSUMED MEAN METHOD = 25.8,STEP DEVIATION METHOD = 25.8.If you want a solution, tell it.

Answer

Answer

Finding Mean using Direct, Assumed Mean and Step Deviation methods

Direct Method:

To find the mean using direct method, we use the formula:

mean = (Σfi*xi) / Σfi

where fi is the frequency of the class interval and xi is the midpoint of the class interval.

Given data:
CI: 0-10, 10-20, 20-30, 30-40, 40-50
fi: 7, 10, 15, 8, 10

Midpoint (xi): 5, 15, 25, 35, 45

Using the formula, we get:
mean = (7*5 + 10*15 + 15*25 + 8*35 + 10*45) / (7+10+15+8+10)
mean = 23

Therefore, the mean of the given data using direct method is 23.

Assumed Mean Method:

To find the mean using assumed mean method, we use the formula:

mean = A + (∑fi*di) / N

where A is the assumed mean, fi is the frequency of the class interval, di is the deviation of the midpoint of the class interval from the assumed mean and N is the total frequency.

Assuming the mean as 25, we get:
di: -20, -10, 0, 10, 20

Using the formula, we get:
mean = 25 + ((7*-20) + (10*-10) + (15*0) + (8*10) + (10*20)) / (7+10+15+8+10)
mean = 23

Therefore, the mean of the given data using assumed mean method is 23.

Step Deviation Method:

To find the mean using step deviation method, we use the formula:

mean = A + (∑fi*h) / N*d

where A is the assumed mean, fi is the frequency of the class interval, h is the deviation of the midpoint of the class interval from the assumed mean divided by the common difference d and N is the total frequency.

Assuming the mean as 25 and the common difference d as 10, we get:
h: -2, -1, 0, 1, 2

Using the formula, we get:
mean = 25 + ((7*-2) + (10*-1) + (15*0) + (8*1) + (10*2)) / (7+10+15+8+10)*10
mean = 23

Therefore, the mean of the given data using step deviation method is 23.

Conclusion:

In this way, we can find the mean of the given data using direct method, assumed mean method and step deviation method.

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