# FIND MEAN MEDIAN MODE AND RANGE OF THE DATA SET

Mean, median and mode are some of the measures of central tendency.

Mean :

The arithmetic mean of a given data is the sum of all observations divided by the number of observations.

Median :

The median is nothing but the middle – or “mid” – of all the values presented in the data set.

There may be odd or even number of data values.

If n is odd, then using the formula

Median   =  (n+1)th term/2

If n is even, then using the formula

Median  =  [(n/2)th term + (n/2+1)th term]/2

Mode :

The observation with the highest frequency is called mode.

Range :

The difference between the largest value and the smallest value is known as range.

Find the mean, median, mode, and range for the data set:

Problem 1 :

1, 3, 4, 5, 9, 9, 11

Solution :

(i)  Mean

By using the mean formula,

Mean = sum of all observations/number of observations

Here, n = 7

= (1 + 3 + 4 + 5 + 9 + 9 + 11)/7

= 42/7

= 6

Mean = 6

(ii) Median

Given data, 1, 3, 4, 5, 9, 9, and 11 in ascending order

So, Median = middle value

Median = 5

(iii) Mode

Given data, 1, 3, 4, 5, 9, 9, 11

In the data, 9 occur the most often value.

So, Mode = 9

(iv)  Range

Range = Large value - small value

= 11 - 1

= 10

Range = 10

Problem 2 :

10, 12, 12, 15, 15, 17, 18, 18, 18, 19

Solution :

(i) Mean

By using the mean formula,

Mean = sum of all observations/number of observations

Here, n = 10

= (10 + 12 + 12 + 15 + 15 + 17 + 18 + 18 + 18 + 19)/10

= 154/10

= 15.4

Mean = 15.4

(ii) Median

Given data, 10, 12, 12, 15, 15, 17, 18, 18, 18, 19 in ascending order

Here, n = 10(even)

By using the median formula,

Median = [(nth/2) term + (n/2+1)th term]/2

= (5th term + 6th term)/2

= (15 + 17)/2

= 32/2

= 16

Median = 16

(iii)  Mode

Given data, 10, 12, 12, 15, 15, 17, 18, 18, 18, 19

In the data, 18 occur the most often value.

So, Mode = 18

(iv) Range

Range = Large value - small value

= 19 - 10

= 9

Range = 9

Problem 3 :

8, 4, 17, 11, 10, 10, 12, 11, 9, 18, 11, 6, 17, 7, 8

Solution :

(i) Mean

By using the mean formula,

Mean = sum of all observations/number of observations

Here, n = 15

= (4 + 6 + 7 + 8 + 8 + 9 + 10 + 10 + 11 + 11 + 11 + 12 + 17 + 17 + 18)/15

= 159/15

= 10.6

Mean = 10.6

(ii)  Median

Given data, 4, 6, 7, 8, 8, 9, 10, 10, 11, 11, 11, 12, 17, 17, 18 in ascending order

So, Median = middle value

Median = 10

(iii)  Mode

Given data, 4, 6, 7, 8, 8, 9, 10, 10, 11, 11, 11, 12, 17, 17, 18

In the data, 11 occur the most often value.

So, Mode = 11

(iv) Range

Range = Large value - small value

= 18 - 4

= 14

Range = 14

Problem 4:

127, 123, 115, 105, 145, 133, 142, 115, 135, 148, 129, 127, 103, 130, 146, 140, 125, 124, 119, 128, 141, 116

Solution :

(i) Mean

By using the mean formula,

Mean = sum of all observations/number of observations

Here, n = 22

= (103 + 105 + 115 + 115 + 116 + 119 + 123 + 124 + 125 + 127 + 127 + 128 + 129 + 130 + 133 + 135 + 140 + 141 + 142 + 145 + 146 + 148)/22

= 2816/22

= 128

Mean = 128

(ii)  Median

Given data, 103, 105, 115, 115, 116, 119, 123, 124, 125, 127, 127, 128, 129, 130, 133, 135, 140, 141, 142, 145, 146, 148 in ascending order

Here, n = 22(even)

By using the median formula,

Median = [(nth/2) term + (n/2+1)th term]/2

= (11th term + 12th term)/2

= (127 + 128)/2

= 255/2

= 127.5

Median = 127.5

(i)  Mode

Given data,

103, 105, 115, 115, 116, 119, 123, 124, 125, 127, 127, 128, 129, 130, 133, 135, 140, 141, 142, 145, 146, 148

In the data, 115, 127 occur the most often values.

So, Mode = 115, 127

(ii) Range

Range = Large value - small value

= 148 - 103

= 45

Range = 45

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