STATISTICSDEVIATION IN VALUES OF

CENTRAL TENDENCY

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STATISTICSDEVIATION IN VALUES OF CENTRAL

TENDENCY

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MEAN, MODE AND MEDIAN

What will happen to the measures of central tendency if we add the same amount to all data values, or multiply each data value by the same amount ?•The mean is equal to the sum of all the values in the data set divided by the number of values in the data set. So, if we have n values in a data set and they have values x1, x2, ..., xn, the sample mean, usually denoted by  (pronounced x bar), is:

OR

•The median is the middle score for a set of data that has been arranged in order of magnitude.•The mode is the most frequent score in our data set.

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When added : Since all values are shifted by the same amount, the measures of central tendency are all shifted by the same amount. If “k” is added to each data value, the mean, mode and median will also increase by “k”.

When added  

PARTICULARS

DATA MEAN

MODE MEDIAN

Original Data Set

Add 5 to each data Value

Add 7 to each data value

6, 7, 8, 10, 12, 14, 14, 15, 16, 20.

11,12,13,15,17,19,19,20,21,25.

13,14,15,17,19,21,21,22,23,27.

12.2

17.2

19.2

14

19

21

13

18

20

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When multiplied : Since all values are affected by the same multiplicative values, the measures of central tendency will also be affected similarly. If each observation is multiplied by “m”, the mean, mode and median will also be multiplied by “m”.

When multiplied

PARTICULARS

DATA MEAN

MODE

MEDIAN

Original Data Set

Multiply 5 times each data Value

Multiply 7 times each data value

6, 7, 8, 10, 12, 14, 14, 15, 16, 20.

30,35,40,50,60,70,70,75,90,100.

42,49,56,70,84,98,98,105,112,140.

12.2

61

85.4

14

70

98

13

90

91

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When subtracted : Since all values are shifted by the same amount, the measures of central tendency are all shifted by the same amount. If “k” is subtracted to each data value, the mean, mode and median will also decrease by “k”.

When subtracted  

PARTICULARS

DATA MEAN

MODE MEDIAN

Original Data Set

Subtract 5 from each data Value

Subtract 2 from each data value

6, 7, 8, 10, 12, 14, 14, 15, 16, 20.

1,2,3,5,7,9,9,10,11,15.

4,5,6,8,10,12,12,13,14,18.

12.2

7.2

10.2

14

9

12

13

8

11

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After observing the examples, we see that

When added : Since all values are shifted by the same amount, the measures of central tendency are all shifted by the same amount. If “k” is added to each data value, the mean, mode and median will also increase by “k”.

When subtracted : Since all values are shifted by the same amount, the measures of central tendency are all shifted by the same amount. If “k” is subtracted to each data value, the mean, mode and median will also decrease by “k”.

When multiplied : Since all values are affected by the same multiplicative values, the measures of central tendency will also be affected similarly. If each observation is multiplied by “m”, the mean, mode and median will also be multiplied by “m”.

When Divided : Since all values are affected by the same multiplicative values, the measures of central tendency will also be affected similarly. If each observation is divided by “m”, the mean, mode and median will also be divided by “m”.

CONCLUTION 

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