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Published on: 18/09/2019
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1.
Find the variance of the following data:
| Classes | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
|---|---|---|---|---|---|
| Frequencies | 15 | 20 | 22 | 27 | 6 |
2.
The mean and S.D. of 100 students of a class in the subjects English, Maths and Science are given below
| Subject | English | Maths | Science |
|---|---|---|---|
| Mean | 51 | 60 | 45 |
| S.D | 12 | 15 | 9 |
Which of the three subjects is more consistent and which is more variable?
3.
The variance of20observations is 5. If each observation is increased by 5, find the new variance.
4.
The following are some particulars of the distribution of weights of boys and girls in a class:
| Boys | Girls | |
| Number | 100 | 50 |
| Mean Weight | 60kg | 45kg |
| Variance | 9 | 4 |
Which of the distributions is more variable?
5.
Suppose that samples balloons from two manufacturers A and B are tested by a trader for bursting pressure as follows;
| Bursting pressure | Number of balloons manufactured by | |
| A | B | |
| 5-10 | 2 | 9 |
| 10-15 | 9 | 11 |
| 15-20 | 29 | 18 |
| 20-25 | 54 | 32 |
| 25-30 | 11 | 27 |
| 30-35 | 5 | 13 |
Which balloons have the highest average bursting pressure?
6.
The coefficient of variation of two distribution are 55% and 70% and their standard deviations are 20 and 18 respectively. What are their arithmetic means?
7.
Find the mean, variance and standard deviation of the following data:
| xi | 3.5 | 4.5 | 5.5 | 6.5 | 7.5 | 8.5 | 9.5 |
| fi | 3 | 7 | 22 | 60 | 85 | 32 | 8 |
8.
Find the mean, variance and standard deviation of the following data: 15, 22, 27, 14, 9, 9, 11, 21
9.
Find the mean, variance and standard deviation of the following data: 62, 65, 57, 56, 69, 51, 62, 60
10.
Find the mean deviation about the median for the following data
34,66,44,30,38,50,42,51,40,60
11.
Find the mean deviation about the mean for the following data
36,72,46,60,45,42,53,49,51,46
12.
Find the standard deviation of first 10 natural numbers
13.
Find the variance of the data 6,5,9,13,12,8 and 10.
14.
Two plants A and B of a factory show results about the number of workers and wages paid to them.
| A | B | |
| Number of workers | 5000 | 6000 |
| Average monthly wages | 2500 | 2500 |
| Variance of distribution of wages | 81 | 100 |
Which plants A or B is the greater variability in individual wages?
15.
The marks obtained by 7 students are 8,9,11 ,13,14,15,21.Find the variance and standard deviation of these marks.
1.
144.06
2.
more consistent: Science, more variable: Maths
3.
5
4.
Boys
5.
B
6.
We know that C.V. = \(\frac { \sigma }{ x } \times 100\)
\(\therefore \ 55=\frac { 20 }{ { x }_{ 1 } } \times 100\Rightarrow \bar { { x }_{ 1 } } =\frac { 2000 }{ 55 } =36.36\)
\(70=\frac { 18 }{ { x }_{ 2 } } \times 100\Rightarrow \bar { { x }_{ 2 } } =\frac { 1800 }{ 70 } =25.71\)
7.
7.09, 1.32, 1.15
8.
16, 38.68, 6.22
9.
60.25, 27.4, 5.23
10.
8.7
11.
7.2
12.
2.87
13.
\(\frac { 52 }{ 7 } \)
14.
Since the average monthly wages in both the plants is same, therefore the plant with greater standard deviation will have more variability. Thus the plant B has greater variability in the individual wages
15.
Here, \(\overline { x } =\frac { 8+9+11+13+14+15+21 }{ 7 } =\frac { 91 }{ 7 } =13marks\)
We make the table from the given data
| Marks(xi)2 | \({ x }_{ i }-\overline { x } \) | \({ ({ x }_{ i }-\overline { x } ) }^{ 2 }\) |
| 8 | -5 | 25 |
| 9 | -4 | 16 |
| 11 | -2 | 4 |
| 13 | 0 | 0 |
| 14 | 1 | 1 |
| 15 | 2 | 4 |
| 21 | 8 | 64 |
| Total | 114 |
Here, n = 7,\(\sum { { ({ x }_{ i }-\overline { x } ) }^{ 2 } } =114\)
\(\therefore \ { \sigma }^{ 2 }=\frac { 1 }{ n } \sum { { ({ x }_{ i }-\overline { x } ) }^{ 2 } } =\frac { 114 }{ 7 } =16.29\)
Also, standard deviation of marks, \(\sigma =\sqrt { 16.29 } =4.04\)
Hence, variance is 16.29 and standard deviation is 4.04
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CBSE 11th Standard CBSE Subjects
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