Question
Find the Value of the following using binomial expansion: $(\sqrt{5}+1)^{5}-(\sqrt{5}-1)^{5}$
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Answer
$352$
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The following data gives the age (in complete years) of $50$ females who committed suicide. Prepare a suitable continuous frequency distribution by taking $9$ classes.
$16,24,20,22,34,40,15,23,31,21,22,24,36,31,21,17,20$, $25,22,23,26,16,18,21,19,52,30,20,27,46,16,21,31,40$, $36,25,24,19,23,21,20,42,43,38,22,24,19,17,21,19 .$
→$16,24,20,22,34,40,15,23,31,21,22,24,36,31,21,17,20$, $25,22,23,26,16,18,21,19,52,30,20,27,46,16,21,31,40$, $36,25,24,19,23,21,20,42,43,38,22,24,19,17,21,19 .$
$20$ 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.
Using all the digits $2, 5, 7, 8$, four digit numbers are to be formed.
$(1)$ How many such numbers can be made ?
$(2)$ How many of them will be even numbers ?
$(3)$ How many of them will be divisible by $5 ?$
$(4)$ How many of them will be greater than $5000 ?$
→$(1)$ How many such numbers can be made ?
$(2)$ How many of them will be even numbers ?
$(3)$ How many of them will be divisible by $5 ?$
$(4)$ How many of them will be greater than $5000 ?$
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 $T_{2}: n_{2}=20 ; \sum d=-20 ; \sum d^{2}=24520$
The following data indicate records of hospital stays (in days) of $30$ patients admitted to hospital: $1,10,2,6,3,4,15,1,5,9,2,4,3,1,10,7,3,5,4,2,4,8,5,3$, $1,9,6,2,3,7$ Find the median of stay. Further convert this information in a continuous frequency distribution (inclusive type) by taking classes of equal length starting from $1-3 .$ Find the median from the frequency distribution and compare it with your earlier answer.
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A transport company has $100$ trucks. These trucks are inspected for maintenance purpose and the following distribution is obtained for the number of defects in the trucks.
Find the range, coefficient of range, quartile deviation, mean deviation and coefficient of mean deviation for the number of defects per truck.
→| No. of Defects | $0$ | $1$ | $2$ | $3-4$ | $5-8$ | $9-14$ | $15-25$ |
| No. of trucks | $8$ | $12$ | $18$ | $24$ | $18$ | $12$ | $8$ |
Find the range, coefficient of range, quartile deviation, mean deviation and coefficient of mean deviation for the number of defects per truck.
The distribution of ages of $48$ persons in an old age home is given below. Which formula will be appropriate to find the mode? Why? Find the modal age of the persons in the old age home using the formula you have chosen.
→| Age (years) | $50 – 60$ | $60 – 65$ | $65 – 70$ | $70 – 85$ | $85 - 100$ |
| No. of person | $6$ | $10$ | $19$ | $9$ | $4$ |