Find the median of the following set of values:

(i) 83, 66, 86, 30, 81.

(ii) 45, 49, 46, 44, 38, 37, 55, 51.

(iii) 70, 71, 70, 68, 67, 69, 70.

(iv) 51, 55, 46, 47, 53, 55, 51, 46.

(i) GIVEN: values are 83, 66, 86, 30, 81

FORMULA USED: if number of values are odd then median is

if number of values are even then median is and

Arrange the values in ascending order

30, 66, 81, 83, 86

The number of observations is 5

Which is odd

Median is term

⇒ Median = term

⇒ Median = 3^rd term

∴ Median = 81

CONCLUSION: The median of given values is 81

(ii) GIVEN: values are 45, 49, 46, 44, 38, 37, 55, 51

FORMULA USED: if number of values are odd then median is

if number of values are even then median is and

Arrange the values in ascending order

37, 38, 44, 45, 46, 49, 51, 55

The number of observations is 8

Which is even

Median is and terms

⇒ Median = and terms

⇒ Median = 4^th and 5th term

∴ Median = Average of 4^th and 5^th term

= = 45.5

CONCLUSION: The median of given values is 45.5

(iii) GIVEN: values are 70, 71, 70, 68, 67, 69, 70

FORMULA USED: if number of values are odd then median is

if number of values are even then median is and

Arrange the values in ascending order

67, 68, 69, 70, 70, 70, 71

The number of observations is 7

Which is odd

Median is term

⇒ Median = term

⇒ Median = 4^th term

∴ Median = 70

CONCLUSION: The median of given values is 70

(iv) GIVEN: values are 51, 55, 46, 47, 53, 55, 51, 46

FORMULA USED: if number of values are odd then median is

If number of values are even then median is and

Arrange the values in ascending order

46, 46, 47, 51, 51, 53, 55, 55

The number of observations is 8

Which is even

Median is and terms

⇒ Median = and terms

⇒ Median = 4^th and 5th term

∴ Median = = 51

CONCLUSION: The median of given values is 51