Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics

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Kerala Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics

Plus One Maths Statistics Three Mark Questions and Answers

Question 1.
Find the mean deviation about the median for the following data: (3 score each)

  1. 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17.
  2. 36, 72, 46, 42, 60, 45, 53, 46, 51, 49.

Answer:
1. Arrange the data in the ascending order we have;
10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18
Here n = 12. So median is the average of 6th and 7th observations.
Therefore; Median, M =\(\frac{13+14}{2}\) = 13.5
Plus One Maths Statistics Three Mark Questions and Answers 1
Mean deviation = \(\frac{\sum_{i=1}^{n}\left|x_{i}-M\right|}{n}=\frac{28}{12}\) = 2.33

2. Arrange the data in the ascending order we have; 36, 42, 45, 46, 46, 49, 51, 53, 60, 72
Here n = 10. So median is the average of 5th and 6th observations.
Therefore; Median, M = \(\frac{46+49}{2}\) = 47.5
Plus One Maths Statistics Three Mark Questions and Answers 2
Mean deviation = \(\frac{\sum_{i=1}^{n}\left|x_{i}-M\right|}{n}=\frac{70}{10}\) = 7.

Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics

Question 2.
The mean and standard deviation of marks obtained by 50 students of a class in three subjects, mathematics, Physics, and Chemistry are given below:
Plus One Maths Statistics Three Mark Questions and Answers 3
Which of the three subject shows the highest variability in marks and which shows the lowest?
Answer:
For Mathematics:
\(\bar{x}\) = 42, σ = 12
∴ CV of Mathematics = \(\frac{12}{42}\) × 100 = 28.57%
For Physics:
\(\bar{x}\) = 32, σ = 15
∴ CV of Physics = \(\frac{15}{32}\) × 100 = 46.88%
For Chemistry:
\(\bar{x}\) = 40.9, σ = 20
∴ CV of Chemistry = \(\frac{20}{40.9}\) × 100 = 48.9%
Thus Chemistry with highest CV shows highest variability and Mathematics with lowest CV shows lowest variability.

Plus One Maths Statistics Four Mark Questions and Answers

Question 1.
Find the mean deviation about the mean for the following data: (4 score each)
1.
Plus One Maths Statistics Three Mark Questions and Answers 4
2.
Plus One Maths Statistics Three Mark Questions and Answers 5
Answer:
1.
Plus One Maths Statistics Three Mark Questions and Answers 6
Plus One Maths Statistics Three Mark Questions and Answers 7
Plus One Maths Statistics Three Mark Questions and Answers 8

Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics

2.
Plus One Maths Statistics Three Mark Questions and Answers 9
Plus One Maths Statistics Three Mark Questions and Answers 10

Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics

Question 2.
Find the mean deviation about the median for the following data: (4 score each)
1.
Plus One Maths Statistics Three Mark Questions and Answers 11
2.
Plus One Maths Statistics Three Mark Questions and Answers 12
Answer:
1.
Plus One Maths Statistics Three Mark Questions and Answers 13
\(\frac{\sum_{i=1}^{n} f_{i}}{2}=\frac{26}{2}\) = 13
The c.f just greater than 13 is 14 and corresponding value of x is 7. Therefore; median, M = 7
Hence; M.D about median
Plus One Maths Statistics Three Mark Questions and Answers 14

2.
Plus One Maths Statistics Three Mark Questions and Answers 15
\(\frac{\sum_{i=1}^{n} f_{i}}{2}=\frac{29}{2}\) = 14.5
The c.f just greater than 14.5 is 21 and corresponding value of x is 30. Therefore; median, M = 30
Hence; M.D about median
Plus One Maths Statistics Three Mark Questions and Answers 16

Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics

Question 3.
Find the mean deviation about the mean for the following data: (4 score each)
1.
Plus One Maths Statistics Three Mark Questions and Answers 17
2.
Plus One Maths Statistics Three Mark Questions and Answers 18
Answer:
1.
Plus One Maths Statistics Three Mark Questions and Answers 19
Plus One Maths Statistics Three Mark Questions and Answers 20

2.
Plus One Maths Statistics Three Mark Questions and Answers 47
Plus One Maths Statistics Three Mark Questions and Answers 21

Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics

Question 4.
Find the mean deviation about the median for the following data: (4 score each)
1.
Plus One Maths Statistics Three Mark Questions and Answers 22
2.
Plus One Maths Statistics Three Mark Questions and Answers 23
Answer:
1.
Plus One Maths Statistics Three Mark Questions and Answers 24
Median class is the class in which the \(\left(\frac{N}{2}\right)^{th}\) observation lies.
\(\frac{N}{2}=\frac{50}{2}\) = 25
Median class = 20 – 30
M = Median
Plus One Maths Statistics Three Mark Questions and Answers 25
Plus One Maths Statistics Three Mark Questions and Answers 26

2.
Plus One Maths Statistics Three Mark Questions and Answers 27

Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics
Median class is the class in which the \(\left(\frac{N}{2}\right)^{th}\) observation lies.
\(\frac{N}{2}=\frac{100}{2}\) = 50
Median class = 35.5 – 40.5
M = Median
Plus One Maths Statistics Three Mark Questions and Answers 28
Plus One Maths Statistics Three Mark Questions and Answers 29

Question 5.
Find the variance and standard deviation of 3, 4, 6, 5, 5, 3, 8, 1, 7, 5
Answer:
Plus One Maths Statistics Three Mark Questions and Answers 30
Plus One Maths Statistics Three Mark Questions and Answers 31
Plus One Maths Statistics Three Mark Questions and Answers 32
\(\frac{259}{10}\) – (4.7)2 = 25.9 – 22.09 = 3.8
Standard Deviation (σ) = \(\sqrt{\text {Variance}}\) = \(\sqrt{3.8}\) =1.95.

Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics

Question 6.
Find the variance and standard deviation of
Plus One Maths Statistics Three Mark Questions and Answers 33
Answer:
Plus One Maths Statistics Three Mark Questions and Answers 34
Plus One Maths Statistics Three Mark Questions and Answers 35
Standard Deviation (σ) = \(\sqrt{\text {Variance}}\)
= \(\sqrt{15.08}\) = 3.88.

Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics

Question 7.
An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following result.
Plus One Maths Statistics Three Mark Questions and Answers 36

  1. Which firm A or B pays larger amount as monthly wages?
  2. Which firm A or B, shows greater variability in individual wages?

Answer:
1. Firm: A
Number of wages earners (n1) = 586
Number of wages earners (\(\bar{x}_{1}\)) = 5253
Total monthly wages = 5253 × 586 = 3078258
Firm: B
Number of wages earners (n1) = 648
Number of wages earners (\(\bar{x}_{1}\)) = 5253
Total monthly wages = 5253 × 648 = 3403944

2. Since both the firms have same mean of monthly wages, so the firm with greater variance will have more variability in individual wages. Thus firm B will have more variability in individual wages.

Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics

Question 8.
The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below:
Plus One Maths Statistics Three Mark Questions and Answers 37
which is more varying, the length or weight?
Answer:
Here,
Plus One Maths Statistics Three Mark Questions and Answers 38
Now
Plus One Maths Statistics Three Mark Questions and Answers 39
C.V of weight = \(\frac{1.38}{5.22}\) × 100 = 26.44
C.V of weight > C.V of length
Thus weight have more variability than length

Plus One Maths Statistics Six Mark Questions and Answers

Question 1.
Find the variance and standard deviation of
Plus One Maths Statistics Three Mark Questions and Answers 40
Answer:
Plus One Maths Statistics Three Mark Questions and Answers 41

Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics
Plus One Maths Statistics Three Mark Questions and Answers 42
Standard Deviation (a) = \(\sqrt{\text {Variance}}\)
= \(\sqrt{223.22}\) = 14.94.

Plus One Maths Statistics Practice Problems Questions and Answers

Question 1.
Find the mean deviation about the mean for the following data: (2 score each)

  1. 4, 7, 8, 9, 10, 12, 13, 17.
  2. 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.

Answer:
1.
Plus One Maths Statistics Three Mark Questions and Answers 43
Plus One Maths Statistics Three Mark Questions and Answers 44

2.
Plus One Maths Statistics Three Mark Questions and Answers 45
Plus One Maths Statistics Three Mark Questions and Answers 46

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