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$M_{ o }=5.3 \ km$
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The following table shows data about the distance travelled: (in km) by a salesman on different days. Find median, $Q_3, D_8, P_{62}$ and interpret them:
We obtain the cumulative frequency distribution for the given frequency distribution.
→| Distance travelled (km) | $0 – 100$ | $100 – 200$ | $200 – 300$ | $300 – 400$ | $400 – 500$ | $500 - 600$ |
| No. of days | $5$ | $18$ | $24$ | $7$ | $5$ | $1$ |
Using binomial expansion show that, $(\sqrt{7}+1)^{5}-$ $(\sqrt{7}-1)^{5}=632$
→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: $(2+\sqrt{5})^{5}+(2-\sqrt{5})^{5}$
→For two groups $T_{1}$ and $T_{2}$, taking $A =25$ the following information are obtained:
Group $T_{1}: n_{1}=10 ; \sum d=30 ; \sum d^{2}=12340$
Group $T_{2}: n_{2}=20 ; \sum d=-20 ; \sum d^{2}=24520$
→Group $T_{1}: n_{1}=10 ; \sum d=30 ; \sum d^{2}=12340$
Group $T_{2}: n_{2}=20 ; \sum d=-20 ; \sum d^{2}=24520$
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 information of profits (in lakh $?$) of $50$ firms in the last year is given below. Find the standard deviation of the profit of the firms.
→Find an appropriate measure of dispersion from the following data. Also find its relative measure.
→| Marks | Less than $10$ | $10 – 20$ | $20 – 30$ | $30 – 40$ | Above $40$ |
| No. of students | $2$ | $4$ | $10$ | $3$ | $1$ |
$20$ workers of a factory get bonus from $₹ 1000$ to $₹ 5000$ as per their performance. Its distribution is as follows.
Obtain coefficient of range, quartile deviation and standard deviation for the bonus.
→| Bonus (₹) | $1000$ | $2000$ | $3000$ | $4000$ | $5000$ |
| No. of workers | $3$ | $5$ | $6$ | $4$ | $2$ |
Obtain coefficient of range, quartile deviation and standard deviation for the bonus.