CBSE 11th Standard Maths Subject Statistics Value Based Questions 2 Marks Questions With Solutions 2021
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CBSE 11th Standard Maths Subject Statistics Value Based Questions 2 Marks Questions With Solutions 2021
11th Standard CBSE
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Reg.No. :
Mathematics
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An analysis of monthly wages paid to workers in two firms A and B belonging to the same industry, give the following result.
Firm A Firm B Number of wages earners 586 648 Mean of monthly wages Rs. 5253 Rs. 5253 Variance of distribution of wages 100 121 Which value is addressed by the firms by paying out larger wages to employees?
(a) -
A school conducted an intelligence test for the students and the winner of the test was to be awarded with a cash prize of Rs. 5000.
The scores of 48 children in an intelligence test are shown in the following frequency table.Score Frequency Score Frequency 71 4 97 4 76 3 101 3 79 4 103 3 83 5 107 3 86 6 110 2 89 5 114 2 90 4 Calculate the variance \({ \sigma }^{ 2 }\) and find out the percentage of children, whose scores lies between \(\overline { x } -\sigma \) and \(\overline { x } +\sigma \).
(a) -
A school conducted an intelligence test for the students and the winner of the test was to be awarded with a cash prize of Rs. 5000.
The scores of 48 children in an intelligence test are shown in the following frequency table.Score Frequency Score Frequency 71 4 97 4 76 3 101 3 79 4 103 3 83 5 107 3 86 6 110 2 89 5 114 2 90 4 What value is shown in this question?
(a) -
In a survey of 44 villages of a state, about the use of LGP as a cooking mode, the following information about the families using LPG was obtained.
Number of families 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Number of villages 6 8 16 8 4 2 Find the mean deviation about median for the following data.
(a) -
In a survey of 44 villages of a state, about the use of LGP as a cooking mode, the following information about the families using LPG was obtained.
Number of families 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Number of villages 6 8 16 8 4 2 Do you think more awareness was needed for the villagers to use LPG as a mode of cooking?
(a)
2 Marks
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CBSE 11th Standard Maths Subject Statistics Value Based Questions 2 Marks Questions With Solutions 2021 Answer Keys
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For Firm A
Number of wages earners = 586
Mean of monthly wages,\(\overline { x } \) = Rs. 5253
Amount paid by firm A = Rs \(\left( 586\times 5253 \right) \) = Rs.3078258
Variance of distribution of wages = 100
\(\therefore \) Standard deviation, \(\sigma \) = \(\sqrt { variance } =\sqrt { 100 } =10\)
Coefficient of variance \(=\frac { \sigma }{ x } \times 100\)
\(=\frac { 10 }{ 5253 } \times 100=0.19\).
For Firm B
Number of wages earners = 648
Mean of monthly wages,\(\overline { x } \) = Rs. 5253
Amount paid by firm B =Rs.\(\left( 648\times 5253 \right) \) = Rs.3403944
Standard deviation \(=\sqrt { 121 } =11\)
\(\therefore \) Coefficient of variance\(=\frac { \sigma }{ x } \times 100\)\(=\frac { 10 }{ 5253 } \times 100=0.21\).
Value of motivating employees by giving financial incentives is addressed by the firm. -
Taking assumed mean, a = 90
Let us make the following table from the given data.xi fi di = xi - a \({ d }_{ i }^{ 2 }\) fidi \({ { f }_{ i }d }_{ i }^{ 2 }\) 71 4 -19 361 -76 1444 76 3 -14 196 -42 588 79 4 -11 121 -44 484 83 5 -7 49 -35 245 86 6 -4 16 -24 96 89 5 -1 1 -5 5 90 4 2 4 8 16 97 4 7 49 28 196 101 3 11 121 33 363 103 3 13 169 39 507 107 3 17 289 51 867 110 2 20 400 40 800 114 2 24 576 48 1152 Total 48 21 6763 Here, \(\Sigma { { f }_{ i }d }_{ i }\) = 21, \(\Sigma { f }_{ i }\) = 48, \(\Sigma { f }_{ i }{ d }_{ i }^{ 2 }\) = 6763
\(\therefore \) Mean, \(\overline { x } =90+\frac { 21 }{ 48 } \) \(\left[ \because \overline { x } =a+\frac { \Sigma { { f }_{ i }d }_{ i } }{ \Sigma { { f }_{ i } } } \right] \)
= 90 + 0.44 = 90.44
and variance, \({ \sigma }^{ 2 }\) = \(\frac { \Sigma { { f }_{ i }d }_{ i }^{ 2 } }{ \Sigma { { f }_{ i } } } \) - \({ \left( \frac { \Sigma { { f }_{ i }d }_{ i } }{ \Sigma { { f }_{ i } } } \right) }^{ 2 }\)
= \(\frac { 6763 }{ 48 } -{ \left( \frac { 21 }{ 48 } \right) }^{ 2 }\)
= 140.896 - 0.191
= 140.705 (approx)
\(\Rightarrow \sigma =\sqrt { 140.705 } =11.86\)
Now, \(\overline { x } -\sigma \) = 90.44 - 11.86
= 78.58.
and \(\overline { x } +\sigma \) = 90.44 + 11.86
= 102.30
\(\therefore \) The number of children whose scores lies between \(\overline { x } -\sigma \) and \(\overline { x } +\sigma \) i.e. between 78.50 and 102.30.
= 4 + 5 + 6 + 5 + 4 + 4 + 3 = 31
Hence, percentage of these children = \(\frac { 31 }{ 48 } \times 100\) = 64.58 (approx). -
Value of encouraging more and more students to participate by announcing a cash prize is shown.
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Let us make the following table from the given data.
Number of families Mid-value (xi) Number of villages (fi) cf |xi - M| fi|xi - M| 0-10 5 6 6 20 120 10-20 15 8 14 10 80 20-30 25 16 30 0 0 30-40 35 8 38 10 80 40-50 45 4 42 20 80 50-60 55 2 44 30 60 Total 44 420 Here, N=44
Now,\(\frac { N }{ 2 } =\frac { 44 }{ 2 } =22\) , which lies in the cumulative frequency of 30, therefore median class is 20-30.
Thus, l = 20, f = 16, cf =14 and h = 10
Hence, \(Median\left( M \right) =l+\frac { \frac { N }{ 2 } -cf }{ f } \times h\)
\(=20+\frac { 22-14 }{ 16 } \times 10=20+\frac { 8 }{ 16 } \times 10\)
\(=30+\frac { 80 }{ 16 } =20+5=25\)
and mean deviation about median
\(\frac { \sum _{ i=1 }^{ 6 }{ { f }_{ i }|{ x }_{ i }-M| } }{ \sum _{ i=1 }^{ 6 }{ { f }_{ i } } } =\frac { 420 }{ 44 } =9.55\). -
There is a need of more awareness among villagers for using LPG as a mode of cooking. Because it will help in keeping the environment clean and will also help in saving of forest.
2 Marks
