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Answer
$M_0=11.64$ Saplings
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The information of the salary of $200$ employees of company is given below. Find the standard deviation of the salary Of the employees :
→| Salary (thousand $Rs.$) | Less than $10$ | Less than $20$ | Less than $30$ | Less than $40$ | Less than $50$ | Less than $60$ | Less than$ 70$ |
| No. of persons | $5$ | $17$ | $47$ | $92$ | $142$ | $179$ | $200$ |
Marks obtained by $50$ students in a test of $50$ marks are as follows :
$\text{16 18 27 31 43 25 28 30 29 15}$
$\text{20 27 31 34 39 41 22 28 31 16}$
$\text{21 29 38 24 30 24 26 17 30 22}$
$\text{28 35 23 18 24 32 37 27 32 38}$
$\text{19 25 33 25 29 25 34 45 26 24}$
$(i)$ From these data, prepare a frequency distribution by taking class length $5$ .
$(ii)$ Obtain 'less than' and 'more than' type cumulative frequency distribution.
$(iii)$ If standard of passing is $20$ marks, then how many students have failed ?
$(iv)$ If at least $30$ marks are required to get first class, find the number of students in this category.
→$\text{16 18 27 31 43 25 28 30 29 15}$
$\text{20 27 31 34 39 41 22 28 31 16}$
$\text{21 29 38 24 30 24 26 17 30 22}$
$\text{28 35 23 18 24 32 37 27 32 38}$
$\text{19 25 33 25 29 25 34 45 26 24}$
$(i)$ From these data, prepare a frequency distribution by taking class length $5$ .
$(ii)$ Obtain 'less than' and 'more than' type cumulative frequency distribution.
$(iii)$ If standard of passing is $20$ marks, then how many students have failed ?
$(iv)$ If at least $30$ marks are required to get first class, find the number of students in this category.
The students of standard $11$ have collected the data about profits (in crore Rs.) of $IT$ companies.
Find Karl Pearson's coefficient of skewness from these data and interpret it.
→Find Karl Pearson's coefficient of skewness from these data and interpret it.
|
Profit (crore₹)
|
$5-7$ | $7-9$ | $9-11$ | $11-13$ | $13-15$ | $15-17$ |
|
No. of companies
|
$5$ | $12$ | $20$ | $8$ | $3$ | $2$ |
Find the Value of the following using binomial expansion: $(3-\sqrt{3})^{4}+(3+\sqrt{3})^{4}$
→The average daily wage of workers of a factory is $Rs. 22.80$. It is $Rs. 25.40$ for the workers of another factory. If the combined average of daily wage of both the factories Is $Rs\ 24$ , find the proportion of workers in both the factories.
→The students of a university were Classified according to faculty and gender. $60\%$ of total $40,000$ students were boys. The number of girls in engineering faculty was three times the number of girls in commerce faculty. $15\%$ and $10\%$ of the total number of university students were boys and girls respectively who belonged to medical faculty. $20\%$ of the total number of students in the university belonged to faculty of Science and among these students, the number of girls were one - seventh of the number of boys. $7\%$ and $17\%$ of the total number of students of arts faculty were boys and girls respectively. $3.75 \%$ of the total number of students of the university belonged to the commerce faculty and the proportion of boys and girls among them was $3 : 7$. Present the above data in an appropriate table.
→
The average monthly salary of employees of a factory is $420$ $Rs.$ . In the factory there are $10$ office staff and remaining are workers. If the average monthly salary of workers Is $350$ $Rs.$ and that of office staff it is $700$$ Rs.$ . Find the number of workers.
→Information regarding the birth rate and death rate of $5$ countries is as under. Present it by a suitable diagram.
→| Country | $U.S.A.$ | Japan | Bharat | Germany | $U.K.$ |
| Birth rate | $16.5$ | $20.8$ | $34.2$ | $16.4$ | $15.2$ |
| Death rate | $10.2$ | $12.2$ | $20.4$ | $10.3$ | $12.0$ |
The frequency distribution of number of accidents due to driving for more than the Prescribed time is given below. Find coefficient of skewness by Bowley’s method.
→| No. of driving hours more than prescribed time | $4$ | $3.5$ | $3$ | $2.5$ | $2$ | $1.5$ | $1$ | $0$ |
| No. of accidents | $5$ | $4$ | $3$ | $2$ | $1$ | $2$ | $2$ | $1$ |