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$M_{ o }=₹ 196$
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Find the middle term in the expansion of $\left(\frac{x^{2}}{2}-\frac{2}{x}\right)^{8}$
→For a sequence of $100$ observations, the mean and standard deviation are $40$ and $10$ respectively. In calculating these measures, two observations were taken as $30$ and $70$ instead of $3$ and $27$ by mistake. Find the corrected mean and corrected standard deviation.
Here, $n=100 ; \overline{ x }=40 ; s=10$
Wrong observation $: 30,70$
True observations $: 3,27$
→Here, $n=100 ; \overline{ x }=40 ; s=10$
Wrong observation $: 30,70$
True observations $: 3,27$
Putting $a=-1$ in the expansion of $(3-2 a)^{3}$ verify both side.
→
Represent the following data through a bar diagram :
→| Stream | Arts | Commerce | Science | Engineering | Other |
| Number of students | $5900$ | $10,200$ | $6000$ | $4500$ | $8000$ |
Define skewed frequency distribution and state its characteristics.
Explain skewness and coefficient of skewness.
Discuss origin and growth of statistics.
The data on quantity of wheat sold (in $\ kg$ ) in a grocery shop during $30$ days are as follows.Prepare a frequency distribution such that class length is $50$ and one of the classes is $250-299$.
$150,290,245,260,100,180,275,390,320,75,140$, $249,195,255,340,190,300,90,295,230,135,250$,$375,165,280,130,330,270,200,240 .$
Answer the following questions on the basis of frequency distribution:
$(1)$ Find the least possible sale of wheat of $20 \%$ days with more sale.
$(2)$ What is the expected sale of $5$ days in the fourth class?
$(3)$ Obtain the boundary points of fifth class.
$(4)$ Find the most possible sale of wheat of $20 \%$ days with less sale.
$(5)$ State the lower limit and upper limit of third class.
→$150,290,245,260,100,180,275,390,320,75,140$, $249,195,255,340,190,300,90,295,230,135,250$,$375,165,280,130,330,270,200,240 .$
Answer the following questions on the basis of frequency distribution:
$(1)$ Find the least possible sale of wheat of $20 \%$ days with more sale.
$(2)$ What is the expected sale of $5$ days in the fourth class?
$(3)$ Obtain the boundary points of fifth class.
$(4)$ Find the most possible sale of wheat of $20 \%$ days with less sale.
$(5)$ State the lower limit and upper limit of third class.
The monthly income (in thousand $Rs$) of $130$ persons living in a certain area is as follows :
Find the median of income.
→| Income (thousand $Rs)$ | Less than $4$ | $4- 8$ | $8- 12$ | $12 – 20$ | $20 – 28$ | $28 – 36$ |
| No. of Persons | $6$ | $14$ | $31$ | $35$ | $28$ | $16$ |