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Example M.N. Elhance’s earnings for the past week were:

Monday          \$ 450
Tuesday          \$ 375
Wednesday     \$ 500
Thursday         \$ 350
Friday             \$ 270

Find his average earning per day.

Solution:

n = 5

\ Arithmetic mean =

Therefore, Elhance’s average earning per day is \$389.

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Short-cut Method :

Sometimes the values of x are very big and in that case, to simplify the calculation the short-cut method is used. For this, first you assume a mean (called as the assumed mean). Let it be A. Now find the deviations of all the values of x from A. We now get a new variable ui = xi - A

Now find

then

Example The expenditure of ten families in dollars are given below :

Family :          A    B    C     D    E     F     G     H     I     J

Expenditure : 300 700 100 750 500 80 120 250 100 370
(in dollars).

Calculate the Arithmetic mean.

Solution: Let the assumed mean be \$ 500. (as. = assume)

Index

4.1 Introduction
4.2 Arithmetic Mean
4.3 Properties of Arithmetic Mean
4.4 Median
4.5 Mode
4.6 Empirical relation between mean, median & mode

Chapter 5