Class 10 Maths Chapter 13 Question Answers - Statistics

ADDITIONAL QUESTIONS SOLVED

VERY SHORT ANSWER TYPE QUESTIONS

Q1. In the following distribution:

The number of families having expenditure range in (Rs) 16000–19000 is:

(i) 15
(ii) 16
(iii)17
(iv) 19

Sol. (iv)19 [∵ 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:

 The modal class is

(i) 15−60
(ii) 30−40
(iii) 20−30
(iv) 10−20

Sol. (ii) 30−40

Q5. The formula    ̄x = a + h [ Σ f_i u_iΣ f_i] 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: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?

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:

Sol. We have:

Here, n = 50 ⇒  n2 = 502  = 25

∵ 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?

 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:

Sol. We have:

Here,  n = 100 ⇒  n2 = 1002  = 50

∴ The median class is 30−40

Q13. Find the class marks of classes 10− 25 and 35− 55.

Sol. We have 

 Class mark of 10 - 25 = 10 + 252  = 352   = 17.5

Class mark of 35 - 55 = 35 + 552  = 902   = 45