Frequency Table

Q.

Q.

Following data gives the number of children in 40 families:
1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.
Represent it in the form of a frequency distribution, taking classes 0-2, 2-4, etc.

Q.

Question 1
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.

Choose the correct answer in each of the following questions:
The class marks of a frequency distribution are 15, 20, 25, 30, .... The class corresponding to the class mark 20 is
(a) 12.5-17.5
(b) 17.5-22.5
(c) 18.5-21.5
(d) 19.5-20.5

Q.

Q.

Explain the difference between a frequency distribution and a cumulative frequency distribution.

Q.

Three coins are tossed 30 times. Each time the number of heads occurring was noted down as follows:
0, 1, 2, 2, 1, 2, 3, 1, 3, 0, 1, 3, 1, 1, 2, 2, 0, 1, 2, 1, 0, 3, 0, 2, 1, 1, 3, 2, 0, 2.
Prepare a frequency distribution table.

Q. Define primary and secondary data.

Q.

Question 2
The distance (in km) of 40 engineers from their residence to their place of work were found as follows:
$\begin{array}{cccccccccc}5& 3& 10& 20& 25& 11& 13& 7& 12& 31\\ 19& 10& 12& 17& 18& 11& 31& 17& 16& 2\\ 7& 9& 7& 8& 3& 5& 12& 15& 18& 3\\ 12& 14& 2& 9& 6& 15& 15& 7& 6& 12\end{array}$
Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main feature do you observe from this tabular representation?

Q.

The water bills (in rupees) of 32 houses in a certain street for the period 01/01/98 to 31/03/98 given below:
56, 43, 32, 38, 56, 24, 68, 85, 52, 47,

35, 58, 63, 74, 27, 84, 69, 35, 44, 75,

55, 30, 54, 45, 67, 95, 72, 43, 65, 35, 59.

Tabulate the data and present the data as a cumulative frequency table using 70-79 as one of the class intervals.

Q. The class size of a distribution is 25 and the first class-interval is 200-224. There are seven class-intervals.

(i) Write the class-intervals.

(ii) Write the class-marks of each intervals.

Q. The blood groups of 36 students of Class IX are recorded as follows: ​A, O, A, O, A, B, O, A, B, A, B, O, B, O, B, O, O, A, B, O, B, AB, O, A, O, O, O, A, AB, O, A, B, O, A, O, B.
Which is the most common and which is the rarest blood group among these students?​

1. B, AB
2. A, AB
3. O, AB
4. AB, A

Q. The following cumulative frequency distribution table shows the daily electricity consumption (in KW) of 40 factories in an industrial state:

Consumption (in KW)	No. of Factories
Below 240 Below 270 Below 300 Below 330 Below 360 Below 390 Below 420	1 4 8 24 33 38 40

(i) Represent this as a frequency distribution table.
(ii) Prepare a cumulative frequency table.

Q.

Define cumulative frequency distribution.

Q.

The marks scored by 40 students of class IX in mathematics are given below:
$$\begin{array}{ccccccccccc}81,& 55,& 68,& 79,& 85,& 43,& 29,& 68,& 54,& 73,& 47,\\ 35,& 72,& 64,& 95,& 44,& 50,& 77,& 64,& 35,& 79,& 52,\\ 45,& 54,& 70,& 83,& 62,& 64& 72,& 92,& 84,& 76& 63\\ 43,& 54,& 38,& 73,& 68,& 52,& 54& & & & \end{array}$$
Prepare a frequency distribution with class size of 10 marks.

Q.

The information collected from individuals is called

1. raw data

2. observation

3. experiment

4. arrayed data

Q.

The median class for the following data is
$$\begin{array}{cccccc}\text{Marks}& \text{Below 10}& \text{Below 20}& \text{Below 30}& \text{Below 40}& \text{Below 50}\\ \text{No. of students}& 5& 10& 23& 31& 40\end{array}$$

1. 10-20

2. 20-30

3. 30-40

4. 40-50

Q.

Give 5 examples of data that you can collect from day to day life and represent them in tabular form.

Q. Three coins were tossed 30 times. Each time the number of heads occurring was noted down as follow:

0	1	2	2	1	2	3	1	3	0
1	3	1	1	2	2	0	1	2	1
3	0	0	1	1	2	3	2	2	0

Prepare a frequency distribution table for the data given above.

Q. Prepare an ungrouped frequency distribution table using the following data.
$\begin{array}{ccccccccccccccccccccc}14,& 16,& 23,& 23,& 25,& 28,& 29,& 30,& 33,& 37,& 37,& 38,& 38,& 38,& 40,& 40,& 40,& 40,& 40,& 41,& 41,\\ 42,& 43,& 44,& 44,& 44,& 45,& 46,& 46,& 47,& 47,& 48,& 49,& 49,& 50,& 50,& 51,& 51,& 52,& 52,& 52,& 55,\\ 55,& 56,& 56,& 56,& 58,& 59,& 60,& 61,& 61,& 62,& 63,& 65,& 66,& 67,& 68,& 68,& 71,& 72,& 73,& 73.& \end{array}$

Q. Tallys are usually marked in a bunch of

(a) 3

(b) 4

(c) 5

(d) 6

Q.

Given below is a cumulative frequency distribution showing the marks secured by $50$ students of a class: Marks Below $20$, Below $40$, Below $60$, Below $80$, Below $100$: Number of students: $17,22,29,37,50$ respectively. Form the frequency distribution table for the data.

Q.

Question 9
A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:
$\begin{array}{cccccccc}2.6& 3.0& 3.7& 3.2& 2.2& 4.1& 3.5& 4.5\\ 3.5& 2.3& 3.2& 3.4& 3.8& 3.2& 4.6& 3.7\\ 2.5& 4.4& 3.4& 3.3& 2.9& 3.0& 4.3& 2.8\\ 3.5& 3.2& 3.9& 3.2& 3.2& 3.1& 3.7& 3.4\\ 4.6& 3.8& 3.2& 2.6& 3.5& 4.2& 2.9& 3.6\end{array}$
Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2−2.5.

Q. The number of hours for which students of a particular class watched television during holidays is shown in the given graph.
We draw the histogram for above frequency table:
Answer the following:

(i) For how many hours did the maximum number of students watch T.V?
(ii) How many students watched TV for less than 4 hours?
(iii) How many students spend more than 5 hours in watching TV?

Q.

Three coins were tossed 30 times. Each time the number of heads occurring was noted down as follow
0 1 2 2 1 2 3 1 3 0
1 3 1 1 2 2 0 1 2 1
3 0 0 1 1 2 3 2 2 0
Prepare a frequency distribution table for the data given above.

Q. Find the mean of the following frequency distribution:

Variable (xi)	10	30	50	70	89
Frequency (fi)	7	8	10	15	10

Q.

3 classmates P, Q and R earned a profit of Rs. 9000. The ratio of capital invested by P and Q is 1 : 2. The ratio of capital invested by Q and R is 4 : 3. Calculate the actual profit each of them earns.

1. Profits of P, Q and R are Rs. 2000, Rs. 4000 and Rs. 9000 respectively

2. Profits of P, Q and R are Rs. 2000, Rs. 4000 and Rs. 3000 respectively

3. Profits of P, Q and R are Rs. 1000, Rs. 4000 and Rs. 3000 respectively

4. Profits of P, Q and R are Rs. 8000, Rs. 4000 and Rs. 3000 respectively

Q. A consumer buys a certain quantity of a good at a price of $Rs.10$ per unit. When price falls to $Rs.8$ per unit, she buys $40$ per cent quantity. Calculate price elasticity of demand.

Q. The marginal utility from the consumption of commodity - X is given in following table:

Units of $X$	$1$	$2$	$3$	$4$	$5$
$M{U}_x$	$10$	$9$	$7$	$3$	$-5$

Calculate total utility for each unit of consumption of commodity - X.

Q.

Following are the ages (in years) of 360 patients, getting medical treatment in a hospital:
$\begin{array}{ccccccc}\text{Age (in years)}& 10-20& 20-30& 30-40& 40-50& 50-60& 60-70\\ \text{Numbr of patients}& 90& 50& 60& 80& 50& 30\end{array}$
Construct the cumulative frequency table for the above data.