This document discusses how measures of central tendency (mean, mode, median) are affected when the same operation is applied to all data values. It shows that if a constant is added to or subtracted from each value, the measures of central tendency are shifted by the same amount. If each value is multiplied or divided by the same constant, the measures of central tendency are multiplied or divided by the same constant. The conclusion is that applying the same operation to all data values proportionally shifts or scales the measures of central tendency.

1. SIRIPURAPU RAMBABU
SIRIPURAPU RAMBABU
MATHS TEACHER

2. STATISTICS
DEVIATION IN VALUES
OF CENTRAL TENDENCY
Get Started ADDING MULTIPLYING SUBTRACTING
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MIND MAP

3. Get start
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4. 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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5. 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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6. 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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7. 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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8. 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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