II. SHORT ANSWER TYPE QUESTIONS
Q1. Find the mode of the data:
Marks  010  1020  2030  3040  4050 
No. of students  3  12  32  20  6 
Sol. Here, modal class is 20â€“30
f_{1} = 32, f_{2} = 20 and f_{0} = 12
Since, the lower limit of the modal class
l = 20
[âˆµ h = 10]
Q2. The percentage marks obtained by 100 students in an examination are given below:
Marks  3035  3540  4045  4550  5055  5560  6065 
Frequency  10  16  18  23  18  8  7 
Find the median from the above data.
Sol. We have:
Marks  Frequency  cf 
3035  10  10 + 0 = 10 
3540  16  16 + 10 = 26 
4045  18  18 + 26 = 44 
4550  23  23 + 44 = 67 
5055  18  18 + 67 = 85 
5560  8  8 + 85 = 93 
6065  7  7 + 93 = 100 
Here,
âˆ´ The median class is 45âˆ’50, such that
l = 45, cf = 44, f = 23 and h = 5
Q3. Write a frequency distribution table for the following data:
Marks  Above 0  Above 10  Above 20  Above 30  Above 40  Above 50 
No. of students  30  28  21  15  10  0 
Sol. Since,
30 âˆ’ 28 = 2
28 âˆ’ 21 = 7
21 âˆ’ 15 = 6
15 âˆ’ 10 = 5
10 âˆ’ 0 =10
The required frequency distribution is:
Marks  Number of students 
010  2 
1020  7 
2030  6 
3040  5 
4050  10 
Total  30 
Q4. Find the median of the following data:
Class interval  020  2040  4060  6080  80100  100120 
Frequency  7  8  12  10  8  5 
Sol.
Class Interval  Frequency  Cumulative frequency 
020  7  7 
2040  8  15 
4060  12  27 
6080  10  37 
80100  8  45 
100120  5  50 
Total  50 

âˆµ Median class is 40â€“60
âˆ´ l = 40, f = 12, CF = 15 and h = 20
Since,