Question

Find the median of the given data if the mean is 4.5.

5, 7, 7, 8, x, 5, 4, 3, 1, 2

Answer 1

Given, mean = 4.5

We know that,

Mean = `"Sum of all observations"/"Total number of observations"`

⇒ `4.5 = (5 + 7 + 7 + 8 + x + 5 + 4 + 3 + 1 + 2)/10`

⇒ 4.5 × 10 = 42 + x

⇒ 45 – 42 = x

∴ x = 3

Now, arrange the data in ascending order

1, 2, 3, 3, 4, 5, 5, 7, 7, 8.

Here, n = 10  ...(Even)

Median = `("Value of"  (n/2)"th observation" + "Value of"  (n/2 + 1)"th observation")/2`

= `("Value of 5th observation" + "Value of 6th observation")/2`

= `(4 + 5)/2`

= `9/2`

= 4.5