Question

Find the median of the 10 observations 36, 33, 45, 28, 39, 45, 54, 23, 56, 25. If another observation 35 is added to the above data, what would be the new median?

Answer 1

Arranging the given 10 observations in ascending order 23, 25, 28, 33, 36, 39, 45, 45, 54, 56

Here number of data n = 10, which is even

∴ Median = `1/2{("n"/2)^"th"  "term" + ("n"/2 + 1)^"th"  "term"}`

= `1/2{(10/2)^"th"  "term" + (10/2 + 1)^"th"  "term"}`

= `1/2{5^"th"  "term" + 6^"th"  "term"}`

= `1/2{36 + 39}`

= `1/2(75)`

= 37.5

∴ Median = 37.5

If 35 is added to the above data then it will be the 5^th term then number of data n = 11, which is odd

∴ Median = `(("n" + 1)/2)^"th"` term

= `((11 + 1)/2)^"th"` term

= `(12/2)^"th"` term

= 6^th term

New median = 36