Grouped Frequency Table

Q. Construct class intervals and frequencies for the following distribution table. Also draw the less than cumulative frequency curve for the same.


[5 marks]

Q. The difference between the upper and lower limits of a class interval is called the ___ of the class interval.

1. size
2. average value
3. mode
4. None of the above

Q. A man bought apples at the rate of 8 for Rs 34 and sold them at the rate of 12 for Rs 57 How many apples should be sold to earn a net profit of Rs 45?

1. 90
2. 100
3. 150
4. 135

Q. Hanif bought one box of $50$ apples for $Rs400$. he sold all the apples at the rate of $Rs10$ each. Was there a profit or loss? What was its percentage?

Q.

a) What is the class size of the given grouped frequency distribution?

b) Which class has the highest frequency?

c) If Sachin scores 20 then in which interval will he be placed in?

d) What is the upper-class limit of the class interval 10-20? [4 MARKS]

$\begin{array}{cc}Runs& Cricketers\\ 0-10& 10\\ 10-20& 3\\ 20-30& 14\\ 30-40& 25\\ 40-50& 11\end{array}$

Q.

a) What is the class size of the given grouped frequency distribution?

b) Which class has the highest frequency?

c) If Sachin scores 20 then in which interval will he be placed in?

d) What is the upper-class limit of the class interval 10-20? [4 MARKS]

$\begin{array}{cc}\text{Runs}& \text{Cricketers}\\ 0-10& 10\\ 10-20& 3\\ 20-30& 14\\ 30-40& 25\\ 40-50& 11\end{array}$

Q. Evaluate: $\frac{{\left(\frac{-3}{5}\right)}^3\times {\left(\frac{9}{25}\right)}^2\times {\left(\frac{-18}{125}\right)}^o}{\left(\frac{-27}{125}\right)\times \left(\frac{-3}{5}\right)}$

1. $-\frac{27}{125}$
2. $\frac{64}{125}$
3. $-\frac{64}{125}$
4. $\frac{27}{125}$

Q. A fruit-seller sells $4$ oranges for Rs. $3$ and gains $50\%$. Find the profit made by selling one orange.

Q. Sarita bought eggs at $R8.40$ a dozen. At what price per hundred must she sell them so as to earn a profit of $15\%$ ?

Q. The following are the marks (out of 100) of 60 students in Mathematics.
16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35,
72, 55, 75, 31, 52, 28, 72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55,
26, 95, 31, 7, 78, 92, 62, 52, 56, 15, 63, 25, 36, 54, 44, 47, 27, 72, 17, 4, 30.
Construct a grouped frequency distribution table with width 10 of each class starting from 0 - 9.

Q. A bought apples at 10 for Rs.75 and sold them at Rs.75 per dozen.Find his loss percent.

Q. The weekly wages (in ₹) of 30 workers in a factory are:
830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840.
Using tally marks, make a frequency table with intervals as 800 – 810, 810 – 820 and so on.

Q. Factorise $a^2(b+c)-(b+c{)}^3$

1. $(b+c)(a^2+(b+c{)}^2)$
2. $(b-c)(a^2-(b+c{)}^2)$
3. $(b+c)(a^2-(b+c{)}^2)$
4. None of these

Q. The difference between the upper and lower limits of a class interval is called the ___ of the class interval.

1. size
2. average value
3. mode
4. None of the above

Q. A fruit vendor buys 300 apples at Rs. 50 per dozen. The vendor sold 200 of them at Rs. 50 per 10 apples. At what rate per apple should the vendor sell the remaining apples to make an overall profit of 12%?.

Q. Evaluate the following by using identities:
(i) ${98}^3$

Q. Factorise: $x^4+y^4-27x^2{y}^2$

1. $(x^2-5xy+y^2)(x^2+5xy-y^2)$
2. $(x^2+xy-y^2)(x^2-5y-y^2)$
3. $(x^2+xy-y^2)(x^2-5x-y^2)$
4. $(x^2+5xy-y^2)(x^2-5xy-y^2)$

Q. Factorize :

1. $(x^2-y^2-xy)(x^2-y^2+xy)$
2. $(x^3-y^3-xy)(x^2-y^2+x)$
3. $(x^2+y^2-xy)(x^2-y^2+y)$
4. $(x^3-y^3-xy)(x^2-y^2+xy)$

Q. Sharad bought one quintal of onions for Rs 2000, Later he sold them all at the rate of rs 18 per kg. Did he make a profit or incur a lost? How much was it?

Q.

State true or false.
If the classes in a grouped frequency distribution are not continuous, we can make them continuous by finding half of the difference between the upper limit of a class and the lower limit of the next class, and then adding the same to all the lower limits and subtracting it from all the upper limits in the distribution.

1. False

2. True

Q. A fruit-seller bought $20$ dozen oranges for Rs. $140.00$. He sold the oranges at the rate of Rs. $7.50$ per dozen. Find his gain or loss.

Q.

Construct a histogram for the following data:

$\begin{array}{cccccccc}\text{Monthly school fee(in Rs):}& 30-60& 60-90& 90-120& 120-150& 150-180& 180-210& 210-240\\ \text{Number of school:}& 5& 12& 14& 18& 10& 9& 4\end{array}$

Q. Devender bought some apples at the rate of $Rs5$ pper apple. He also bought an equal number of bamanas at the rate of $Rs2$ per banana. He sold the apples at a profit of $20\%$ and the bananas at a loss of $5\%$, but still made an overall profit of $Rs360$ after selling all the fruits. What is the number of apples he had purchase?

Q. In a meseum, the entrance ticket costs Rs. $250$. In Vacation, the cost of the ticket is reduced, there by increasing the sale by $50$ $\%$, but it was found that the collection is decreased by $17.5$ $\%$. What is the deduction in the ticket price?

1. Rs. $1125$
2. Rs. $115.5$
3. Rs. $100$
4. Rs. $110$

Q. The marks obtained by 36 students in a test in statistics (out of 50) are as below.
$\begin{array}{cccccccccccc}3& 5& 1& 15& 35& 45& 23& 31& 40& 21& 13& 15\\ 20& 47& 48& 42& 34& 43& 45& 33& 37& 11& 13& 27\\ 18& 12& 37& 39& 38& 16& 13& 18& 5& 41& 47& 43\end{array}$
Construct a frequency distribution table with equal class intervals, one of them being 10-20(20 is not included).

Q.

a) What is the class size of the given grouped frequency distribution?

b) Which class has the highest frequency?

c) If Sachin scores 20 then in which interval will he be placed in?

d) What is the upper-class limit of the class interval 10-20? [4 MARKS]

$\begin{array}{cc}\text{Runs}& \text{Cricketers}\\ 0-10& 10\\ 10-20& 3\\ 20-30& 14\\ 30-40& 25\\ 40-50& 11\end{array}$

Q. Factorise the following expression-
$k^4+4k^2{m}^2+4m^4$

Q. A fridge has a listed price of Rs. 16, 000. Successive discounts of 10 % and 20 % are given on its listed price. Sales tax is then charged at 30 %. Ravi bought it for Rs. S which includes the sales tax. Find S.

Q. Profit earned by selling an article for Rs. $1,060$ is $20$% more than the loss incurred by selling the article for Rs. $950$. At what price should the article be sold to earn $20$% profit?

1. Rs. $1000$
2. Rs. $1150$
3. Rs. $1,200$
4. Rs. $1,250$

Q. Vikas goes to the market for buying some fruits. If the cost of $6$ apples and $3$ bananas is $Rs.43.50$. But $5$ apples and $7$ banana costs $Rs.61$. How much does $1$ banana and $1$ apple cost together?

1. $Rs.8$
2. $Rs.9.75$
3. $Rs.10$
4. $Rs.11.25$