The marks obtained (out of 50) by 40 students in a test are given below:

28, 31, 45, 03, 05, 18, 35, 46, 49, 17, 10, 28, 31, 36, 40, 44, 47, 13, 19, 25, 24, 31, 38, 32, 27, 19, 25, 28, 48, 15, 18, 31, 37, 46, 06, 01, 20, 10, 45, 02.

(i) Taking class intervals 1 – 10, 11 – 20, .., construct a tally chart and a frequency distribution table.

(ii) Convert the above distribution to continuous distribution.

(iii) State the true class limits of the third class.

(iv) State the class mark of the fourth class.

(i) The frequency distribution table for given grouped data is :

(ii) Adjustment factor = (Lower limit of one class - Upper limit of previous class) / 2

$= \dfrac{11 - 10}{2} = \dfrac{1}{2}$ = 0.5

Subtracting the adjustment factor (0.5) from all the lower limits and add the adjustment factor (0.5) to all the upper limits.

Continuous frequency distribution for the given data is :

(iii) Third class : 20.5 - 30.5

Hence, lower limit : 20.5 and upper limit : 30.5

(iv) Class mark = $\dfrac{\text{Lower limit + Upper limit}}{2}$

= $\dfrac{30.5 + 40.5}{2} = \dfrac{71}{2}$ = 35.5

Hence, class mark of fourth class = 35.5