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Mean, Median, Mode Calculations

The document defines and provides examples for calculating various measures of central tendency including the mean, median, mode, and mean of a frequency distribution. It first defines the arithmetic mean as the central value that lies between the highest and lowest values. It provides the formula for calculating the mean as the sum of all observations divided by the number of observations. It then defines calculating the mean of a frequency distribution by multiplying each observation by its frequency, summing the products, summing the frequencies, and dividing the total of the products by the total of the frequencies. Additional sections define the median as the middle value when observations are written in order of size, and the mode as the value with the highest frequency. The

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Saransh
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251 views29 pages

Mean, Median, Mode Calculations

The document defines and provides examples for calculating various measures of central tendency including the mean, median, mode, and mean of a frequency distribution. It first defines the arithmetic mean as the central value that lies between the highest and lowest values. It provides the formula for calculating the mean as the sum of all observations divided by the number of observations. It then defines calculating the mean of a frequency distribution by multiplying each observation by its frequency, summing the products, summing the frequencies, and dividing the total of the products by the total of the frequencies. Additional sections define the median as the middle value when observations are written in order of size, and the mode as the value with the highest frequency. The

Uploaded by

Saransh
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
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n

a
i
d
e
M
,
n
a
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M
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o
&M

Arithmetic Mean
Mean is number which lies
between the highest and the
lowest value. In other words, it
represents the central value of a
group of observations or data.
Mean= Sum of observations/number
of observations.

Mean (frequency
distribution)
1. Multiply each observation (x) by its

corresponding frequency (f) and


denote it by (f *x).
2. Find the sum of all products obtained
above and denote by( f *x).
3. Find the sum of all frequencies and
denote it by f.
4. Divide the sum of all the products by
the sum of all frequencies, i.e., f * x
by f.

Median
The median is the value which is strictly
in the middle of the list of the
observations when written in order of
size. It is also a measure of central
tendency.

Mode
The value which occurs the most is
called mode. In other words, the
value of the observation which has
maximum frequency in a data is
called mode.

n
o
i
t
s
e
u
Q
Time!!

1. The mean of 10 numbers is

32. If one number is excluded,


mean of the remaining
numbers becomes 27. Find
the excluded number.

SolutionMean of 10 numbers
=32
Sum of 10 numbers =32*10=320
Mean of 9 numbers =30
Sum of 9 numbers =27*9=243
Excluded number =320-243 = 77

2.

The mean of 7 numbers is 25. If


one number is excluded, mean of
new set of numbers becomes 27.
find the included number.

SolutionMean of 7 numbers =25


Sum of 7 numbers =25*7=175
Mean of 8 numbers =27
Sum of 8 numbers =27*8=216
Included number =216-175=41

3. Calculate the mean for the following

dataHeight
(in cm)

140

142

143

145

148

150

No. of
student
s

10

15

SolutionHeight (x)

Frequency (f)

Product(f*x)

140
142
143
145
148
150

2
6
10
15
4
3

280
852
1430
2175
592
450

Total =

40

5779

Mean= fx / f =5779/40 =144.475

4. Calculate the mean of the following


dataMarks

No. of
student
s

10

11

12

13

14

15

10

SolutionMarks (x)

No. of
students (f)

Product (f*x)

32

45

10

30

11

88

12

48

13

10

130

14

70

15

15

Total =

40

458

Mean= fx / f = 458/40 = 11.45

5. Find the median of 5, 9, 6, 4, 7, 2, 8

SolutionArranging the numbers in ascending


order we get - 2, 4, 5, 6, 7, 8, 9.
There are 7 observations. The middle
(i.e., 7+1/2 th) observation is 6.
Hence median= 6.

6. Find the median of2, 5, 3, 2, 4, 5, 2, 4, 6, 8, 7, 9, 7

SolutionArranging the numbers in ascending order


we get 2, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9.
There are 13 observations. The middle
(i.e.,13+1/2th ) observation is 5.
Hence median= 5

7. Find the median of11, 10, 12, 9, 8, 16, 15, 14

SolutionAfter arranging in ascending order, we get


8, 9, 10, 11, 12, 14, 15, 16.
There are 8 observations. There is no
strict middle observation. Here median is
average of (8/2) 4th and (8/2+1) 5th
observations.
Fourth observation= 11
Fifth observation= 12
Median= 11+12/2 = 11.5

8. Find the median of2, 3, 4, 3, 2, 4, 6, 5, 7, 6, 5, 9, 8,


10

SolutionAfter arranging in ascending order, we


get
2, 2, 3, 3, 4, 4, 5. 5, 6, 6, 7, 8, 9, 10.
Here we have 14 observations. The 7 th
and 8th observation are in the middle.
7th observation = 5
8th observation = 5
Median = 5+5/2 = 5

9. Find the mode-

SolutionCarnation is the mode.

10. Find the mode-

SolutionChocolate bar is the mode.

11. Find the mode-

SolutionThe month of June is the mode.

Efforts
bySaransh
Gautam

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