In this section, we shall deal with the variance of a discrete frequency distribution, which is illustrated with examples. Students can use this exercise as a model to improve their conceptual knowledge and understand the different methodologies used to solve the problems. Students can refer to RD Sharma Class 11 Maths Solutions, which is one of the best reference guides they can depend upon. Solutions here are developed by the subject experts in a simple manner to help increase students’ confidence, which plays a major role in their board exams. The links to the solutions of this exercise can be accessed in the RD Sharma Class 11 Maths PDF, which is available in the below links.
RD Sharma Solutions for Class 11 Maths Exercise 32.5 Chapter 32 – Statistics
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Access answers to RD Sharma Solutions for Class 11 Maths Exercise 32.5 Chapter 32 – Statistics
EXERCISE 32.5 PAGE NO: 32.37
1. Find the standard deviation for the following distribution:
| x: | 4.5 | 14.5 | 24.5 | 34.5 | 44.5 | 54.5 | 64.5 |
| f: | 1 | 5 | 12 | 22 | 17 | 9 | 4 |
Solution:
= 100 [1.857 – 0.0987]
= 100 [1.7583]
Var (X) = 175.83
2. Table below shows the frequency f with which ‘x’ alpha particles were radiated from a diskette
| x: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| f: | 51 | 203 | 383 | 525 | 532 | 408 | 273 | 139 | 43 | 27 | 10 | 4 | 2 |
Calculate the mean and variance.
Solution:
3. Find the mean, and standard deviation for the following data:
(i)
| Year render: | 10 | 20 | 30 | 40 | 50 | 60 |
| No. of persons (cumulative) | 15 | 32 | 51 | 78 | 97 | 109 |
Solution:
(ii)
| Marks: | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| Frequency: | 1 | 6 | 6 | 8 | 8 | 2 | 2 | 3 | 0 | 2 | 1 | 0 | 0 | 0 | 1 |
Solution:
4. Find the standard deviation for the following data:
(i)
| x: | 3 | 8 | 13 | 18 | 23 |
| f: | 7 | 10 | 15 | 10 | 6 |
Solution:
(ii)
| x: | 2 | 3 | 4 | 5 | 6 | 7 |
| f: | 4 | 9 | 16 | 14 | 11 | 6 |
Solution:
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