Question

The ages of 80 students (above 8 years) of a school are measured and tabulated as below:

Age (in years)	8 – 10	below 12	below 14	below 16	below 18
Number of students	7	15	29	68	80

Construct a frequency distribution table for the above data. Also, answer the following questions:

1. How many students have at least 16 years age but less than 18 years? 
2. How many students have at most 14 years age?

Answer 1

Given: Ages of 80 students (above 8 years) are tabulated as: 8 – 10 : 7; below 12 : 15; below 14 : 29; below 16 : 68; below 18 : 80.

Step-wise calculation:

1. Take class intervals as:

8 – 10

10 – 12

12 – 14

14 – 16

16 – 18

2. Frequencies from cumulative (subtract previous cumulative):

8 – 10:

f₁ = 7   ...(Given)

10 – 12:

f₂ = (Below 12) – f₁ 

= 15 – 7

= 8

12 – 14:

f₃ = (Below 14) – (Below 12)

= 29 – 15

= 14

14 – 16:

f₄ = (Below 16) – (Below 14)

= 68 – 29

= 39

16 – 18:

f₅ = (Below 18) – (Below 16)

= 80 – 68

= 12

Frequency distribution table:

Age (in years)	Number of students
8 – 10	7
10 – 12	8
12 – 14	14
14 – 16	39
16 – 18	12
Total	80

i. Students with at least 16 but less than 18 years

= Frequency of 16 – 18 

= 12

ii. Students with at most 14 years age

= Cumulative up to 14

= 29