Solution:

We write the variates in cumulative frequency table.

(i) Here number of observations, n = 48 which is even.

So median = ½ ( n/2 ^th term + ((n/2)+1)^th term)

= ½ (48/2 ^th term + ((48/2)+1)^th term)

= ½ (24 ^th term + (24+1)^th term)

= ½ (24 ^th term + 25^th term)

= ½ (22+22) [Since all observations from 19^th to 27^th are 22]

= ½ ×44

= 22

Hence the median is 22.

(ii) Lower quartile, Q₁ = (n/4) ^th term

= (48)/4

= 12 ^th term

= 20

Hence the lower quartile is 20.

(iii)Upper quartile, Q₃ = (3n/4) ^th term

= (3×48/4) ^th term

= (3×12)^th term

= 36 ^th term

= 27

Hence the upper quartile is 27.

(iv)Interquartile range = Q₃-Q₁

= 27-20

= 7

Hence the Interquartile range is 7.