Question

1. Calculate arithmetic mean by direct, assumed mean and step deviation
the following data.
40, 50, 55, 78, 58
has​

Answer 1

Let us look at the answer:

Explanation:

The given observations are: 40, 50, 55, 58, 78

The mean can be found by three ways,

• direct method
• assumed mean
• step-deviation method

direct method: X = sum of observation/ number of observations

  X = 40+50+55+58+78 / 5 = 281/5 = 56.2

  Assumed method  A = 55

Answer 2

arithmetic mean  = 56.2

Explanation:

given data

x = 40, 50, 55, 78, 58

N = 5

to find out

arithmetic mean

solution

first we get here arithmetic mean by direct method that is express as

$\bar x = \frac{\sum{x}}{N}$     ...................1

put here value by given table solution of sum of x and N

$\bar x = \frac{281}{5}$

$\bar x$  = 56.2

and

now we get here by assumed mean method that is express as

$\bar x = A + \frac{\sum{d}}{N}$    .......................2

put here value and we get

$\bar x = 40 + \frac{81}{5}$

$\bar x$  = 56.2

and

now we get here by step deviation method that is express as

$\bar x = A + \frac{\sum{d'}}{N} \times c$      ................3

put here value and we get

$\bar x = 40 + \frac{8.1}{5} \times 10$  

$\bar x$ = 56.2

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arithmetic mean

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