ADDITIONAL QUESTIONS SOLVED
VERY SHORT ANSWER TYPE QUESTIONS
Q1. In the following distribution:
Monthly expenditure  Number of families 
Expenditure more than Rs 10,000  100 
Expenditure more than Rs 13,000  85 
Expenditure more than Rs 16,000  69 
Expenditure more than Rs 19,000  50 
Expenditure more than Rs 22,000  33 
Expenditure more than Rs 25,000  15 
The number of families having expenditure range in (Rs) 16000–19000 is:
(i) 15
(ii) 16
(iii)17
(iv) 19
Sol. (iv)1 9 [∵ 69 − 50 = 19]
Q2. Construction of a cumulative frequency table is useful in determining the (i) mean (ii) mode (iii) median (iv) all the above
(i) mean
(ii) mode
(iii) median
(iv) all the above
Sol. (iii) median
Q3. The abscissa of the point of interaction of the ‘less than type’ and of the ‘more than type’ comutative frequency curve of grouped data gives its:
(i) mode
(ii) mean
(iii) median
(iv) All the three above
Sol. (iii) median.
Q4. For the following distribution:
Marks  Number of Students 
Below 10  3 
Below 20  12 
Below 30  27 
Below 40  57 
Below 50  75 
Below 60  80 
The modal class is
(i) 15−60
(ii) 30−40
(iii) 20−30
(iv) 10−20
Sol. (ii) 30−40
Q5. The formula is used to determine:
(i) mean
(ii) mode
(iii) median
(iv) all the three above of grouped data.
Sol. (i) mean
Q6. Consider the following distribution:
Marks obtained  Number of students 
More than or equal to 0  63 
More than or equal to 10  58 
More than or equal to 20  55 
More than or equal to 30  51 
More than or equal to 40  48 
More than or equal to 50  42 
The frequency of the class 30−40 is:
(i) 51
(ii) 48
(iii) 4
(iv) 3
Sol. (iv) 3
Q7. Fill in the blank:
Mode = (..................) − 2 (Mean)
Sol. Mode = 3 (median) − 2 (Mean)
Q8. What is the modal class of the following frequency distribution?
Classes  010  1020  2030  3040  4050  5060 
Frequencies  5  8  13  38  30  4 
Sol. The Highest frequency 38 corresponds to 30−40.
∴ The modal class is 30–40.
Q9. Write the empirical relation between mean, mode and median.
Sol. The three measures i.e., mean, mode and median are connected by the following empirical relation:
Mode = 3 Median – 2 Mean
Q10. Write the median class of the following distribution:
Class  Frequency 
010  4 
1020  4 
2030  8 
3040  10 
4050  12 
5060  8 
6070  4 
Sol. We have:
Class  Frequency  Cumulative Frequency 
010  4  4 + 0 = 4 
1020  4  4 + 4 = 8 
2030  8  8 + 8 = 16 
3040  10  16 + 10 = 26 
4050  12  26 + 12 = 38 
5060  8  38 + 8 = 44 
6070  4  46 + 4 = 50 
Here,
∵ 25 is cumulative frequency corresponding to the class 30−40.
∴ Median class is 30−40.
Q11. What is the modal class of the following frequency distribution?
Age (in years)  0 10  10  20  20  30  30  40  40  50  50  60 
Number of Patients  16  13  6  11  27  18 
Sol. Here, the maximum class frequency is 27 and the class corresponding to this frequency is 40−50.
∴ The modal class is 40−50.
Q12. Find the median class of the following data:
Marks  0 10  10  20  20  30  30  40  40  50  50  60 
Frequency  8  10  12  22  30  18 
Sol. We have:
Marks obtained  Frequency  Cumulative Frequency 
010  8  8 + 0 = 8 
1020  10  8 + 10 = 18 
2030  12  18 + 12 = 30 
3040  22  30 + 22 = 52 
4050  30  52 + 30 = 82 
5060  18  82 + 18 = 100 
Here,
∴ The median class is 30−40
Q13. Find the class marks of classes 10− 25 and 35− 55.
Sol.
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1. What is statistics? 
2. What are the different types of data? 
3. What is the importance of statistics in everyday life? 
4. What is the difference between a population and a sample? 
5. How do we measure central tendency in statistics? 

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