Question

Observe the given frequency table to answer the following:

Class Interval	20 - 24	25  29	30 - 34	35 - 39	40 - 44	45 - 49
Frequency	6	12	10	15	9	2

a. The true class limits of the fifth class.
b. The size of the second class.
c. The class boundaries of the fourth class.
d. The upper and lower limits of the sixth class.
e. The class mark of the third class.

Answer 1

a. Fifth class : 40 - 44
Since classes are inclusive, we have

Adjustment factor

= `(25 - 24)/(2)`

= `(1)/(2)`
= 0.5
∴ True lower limit of 5^th class = 40 - 0.5 = 39.5
True Upper limit of 5^th class = 44 + 0.5 = 44.5.

b. Size of class 25 - 29 = 29.5 - 24.5 = 5.

c. True lower limit of 4^th class = 35 - 0.5 = 34.5
True Upper limit of 4^th class = 39 + 0.5 = 39.5
∴ Class boundaries of 4th class are 34.5 and 39.5.

d. Lower limit of 6^th class = 45 - 0.5 = 44.5
Upper limit of 6^th class = 49 + 0.5 = 49.5.

e. True lower limit of 3^rd class = 30 - 0.5 = 29.5

True Upper limit of 3^rd class = 34 + 0.5 = 34.5

∴ Class mark

= `(29.5 + 34.5)/(2)`
= 32.