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$\bar{x}=147$ Cups
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The data related to variations in the price of a share for $30$ days in a share market are as under. Prepare an exclusive continuous of one of classification having class limits the classes as $18.5-20.5$.
$10.50,14.70,17.20,15.20,19.20,15.80,19.30$, $18.40,18.70,14.90,18.50,16.90,12.50,13.60,12.50$, $18.50,14.00,16.20,13.30,3.30,17.6020 .2014 .50$, $20.80,14.50,20.50,10.50,18.60,18.60,14.90$
On the basis of this frequency distribution, answer the following questions:
$(1)$ What is mid value of the 4 th class?
$(2)$ Find the number of days during which the price of share is at the most $Rs. 16.50$.
$(3)$ Find the number of days during which the price of share is at least $Rs. 19.50$.
→$10.50,14.70,17.20,15.20,19.20,15.80,19.30$, $18.40,18.70,14.90,18.50,16.90,12.50,13.60,12.50$, $18.50,14.00,16.20,13.30,3.30,17.6020 .2014 .50$, $20.80,14.50,20.50,10.50,18.60,18.60,14.90$
On the basis of this frequency distribution, answer the following questions:
$(1)$ What is mid value of the 4 th class?
$(2)$ Find the number of days during which the price of share is at the most $Rs. 16.50$.
$(3)$ Find the number of days during which the price of share is at least $Rs. 19.50$.
The distribution of marks obtained by $60$ students in an examination is as follows. Find coefficient of skewness by Karl Pearson's method and state the type of skewness.
| Marks of students | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ | $50-60$ | $Total$ |
| No. of students | $5$ | $12$ | $38$ | $38$ | $20$ | $7$ | $120$ |
The following table shows the monthly expense for entertainment in a group of $100$ students. Find the median of this expense.
→| Expense $(₹)$ | Less than $200$ | $200-400$ | $400-600$ | $600-700$ | $700-800$ | $900$ and above |
| No. of students | $8$ | $23$ | $40$ | $17$ | $7$ | $5$ |
Find the Value of the following using binomial expansion: $(3-\sqrt{3})^{4}+(3+\sqrt{3})^{4}$
→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.
→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 distribution of sales (in thousand tons) of $400$ companies during the year $2014 – 15$ is as follows.
Find skewness and its coefficient from these data and state the type of skewness.
→Find skewness and its coefficient from these data and state the type of skewness.
| Sales (thousand tons) | Less than $20$ | $20 – 40$ | $40 – 50$ | $50 - 75$ | $75 – 90$ | $90 – 120$ | $120$ and above |
| No. of companies | $30$ | $70$ | $125$ | $100$ | $40$ | $20$ | $15$ |
Following data are obtained for two groups $G_{1}$ and $G_{2}$ Find combined mean and combined standard deviation.
Group $G_{1}: n_{1}=20 ; \bar{x}_{1}=35 ; S_{1}^{2}=15$
Group $G_{2}: n_{2}=30 ; \bar{x}_{2}=40 ; S_{2}^{2}=12$
→Group $G_{1}: n_{1}=20 ; \bar{x}_{1}=35 ; S_{1}^{2}=15$
Group $G_{2}: n_{2}=30 ; \bar{x}_{2}=40 ; S_{2}^{2}=12$
The information of number of mobiles phones sold in last $35$ days in a mobile shop is given below. Find the co-efficient of standard deviation of number of mobile phones sold. (Use short-cut method).
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