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) 16000â€“19000 is:
(i) 15
(ii) 16
(iii)17
(iv) 19
Sol. (iv)1 9 [âˆµ 69 âˆ’ 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 â€˜less than typeâ€™ and of the â€˜more than typeâ€™ 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) 15âˆ’60
(ii) 30âˆ’40
(iii) 20âˆ’30
(iv) 10âˆ’20
Sol. (ii) 30âˆ’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 30âˆ’40 is:
(i) 51
(ii) 48
(iii) 4
(iv) 3
Sol. (iv) 3
Q7. Fill in the blank:
Mode = (..................) âˆ’ 2 (Mean)
Sol. Mode = 3 (median) âˆ’ 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 30âˆ’40.
âˆ´ The modal class is 30â€“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 â€“ 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,
âˆµ 25 is cumulative frequency corresponding to the class 30âˆ’40.
âˆ´ Median class is 30âˆ’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 40âˆ’50.
âˆ´ The modal class is 40âˆ’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,
âˆ´ The median class is 30âˆ’40
Q13. Find the class marks of classes 10âˆ’ 25 and 35âˆ’ 55.
Sol.
Q14. What measure of central tendency is obtained graphically as the x-coordinate of the point of intersection of the two ogives for grouped data?
Sol. When two ogives intersect each other at a point and from this point, if we draw a perpendicular on the x-axis, then the point at which it cuts the x-axis gives us the median.
Q15. What is the median class of the following grouped data?
Class | Frequency |
128-135 | 8 |
135-142 | 5 |
142-149 | 9 |
149-156 | 12 |
156-163 | 5 |
163-170 | 1 |
Sol. We have:
Class | Frequency | Cumulative Frequency |
128-135 | 8 | 8 + 0 = 8 |
135-142 | 5 | 5 + 8 = 13 |
142-149 | 9 | 9 + 13 = 22 |
149-156 | 12 | 12 + 22 = 34 |
156-163 | 5 | 5 + 34 = 39 |
163-170 | 1 | 1 + 39 = 40 |
n = 40
â‡’ The median class is 142-149.