Arithmetic mean or mean

Arithmetic mean or mean

    • Arithmetic mean or simply the mean of a variable is defined as the sum of the observations divided by the number of observations. It is denoted by the symbol If the variable x assumes n values x1, x2 … xn then the mean is given by
       
    Arithmetic mean or mean
    mean

    Example 1

    • Calculate the mean for pH levels of soil 6.8, 6.6, 5.2, 5.6, 5.8

    Solution

    Ex
    Grouped Data

    • The mean for grouped data is obtained from the following formula

    Grouped Data

    • where x = the mid-point of individual class
    • f = the frequency of individual class
    • n = the sum of the frequencies or total frequencies in a sample.

    Short-cut method

    Short-cut method

    Where where

    A = any value in x
    n = total frequency
    c = width of the class interval

    Example 2

    • Given the following frequency distribution, calculate the arithmetic mean

    Marks 64 63 62 61 60 59
    Number of Students 8 18 12 9 7 6

    Solution
    X F Fx D=x-A Fd
    64 8 512 2 16
    63 18 1134 1 18
    62 12 744 0 0
    61 9 549 -1 -9
    60 7 420 -2 -14
    59 6 354 -3 -18
    60 3713 -7

    Direct method

    Direct method

    Direct_method

    Short-cut method

    Short-cut method

    Here A = 62

    solution

    Example 3

    • For the frequency distribution of seed yield of seasamum given in table, calculate the mean yield per plot.

    Yield per plot n(in g)

    64.5-84.5

    84.5-104.5

    104.5-124.5

    124.5-144.5

    No of plots

    3

    5

    7

    20


    Solution

    Yield ( in g)

    No of Plots (f)

    Mid X

    Fd

    64.5-84.5

    3

    74.5

    -1

    -3

    84.5-104.5

    5

    94.5

    0

    0

    104.5-124.5

    7

    114.5

    1

    7

    124.5-144.5

    20

    134.5

    2

    40

    Total

    35



    44


    A=94.5
    The mean yield per plot is
    Direct method:

    mean yield

    = 1 =119.64 gms

    Shortcut method

    1

    ans

    Merits and demerits of Arithmetic mean
    Merits

    • It is rigidly defined.
    • It is easy to understand and easy to calculate.
    • If the number of items is sufficiently large, it is more accurate and more reliable.
    • It is a calculated value and is not based on its position in the series.
    • It is possible to calculate even if some of the details of the data are lacking.
    • Of all averages, it is affected least by fluctuations of sampling.
    • It provides a good basis for comparison.

    Demerits

    • It cannot be obtained by inspection nor located through a frequency graph.
    • It cannot be in the study of qualitative phenomena not capable of numerical measurement i.e.
    • Intelligence, beauty, honesty etc.,
    • It can ignore any single item only at the risk of losing its accuracy.
    • It is affected very much by extreme values.
    • It cannot be calculated for open-end classes.
    • It may lead to fallacious conclusions, if the details of the data from which it is computed are
    • not given

Last modified: Friday, 16 March 2012, 5:02 PM