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 | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
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 |
0-10 | 4 |
10-20 | 4 |
20-30 | 8 |
30-40 | 10 |
40-50 | 12 |
50-60 | 8 |
60-70 | 4 |
Sol. We have:
Class | Frequency | Cumulative Frequency |
0-10 | 4 | 4 + 0 = 4 |
10-20 | 4 | 4 + 4 = 8 |
20-30 | 8 | 8 + 8 = 16 |
30-40 | 10 | 16 + 10 = 26 |
40-50 | 12 | 26 + 12 = 38 |
50-60 | 8 | 38 + 8 = 44 |
60-70 | 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 |
0-10 | 8 | 8 + 0 = 8 |
10-20 | 10 | 8 + 10 = 18 |
20-30 | 12 | 18 + 12 = 30 |
30-40 | 22 | 30 + 22 = 52 |
40-50 | 30 | 52 + 30 = 82 |
50-60 | 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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