FIND MEAN MEDIAN MODE AND RANGE OF THE DATA SET

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

= (5^th term + 6^th 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 = [(n^th/2) term + (n/2+1)^th term]/2

= (11^th term + 12^th 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