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Published on: 03/08/2019
Data Handling
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1.
Study the following frequency table and answer the questions given below.
(i) What is the class interval?
(ii) Which class has the lowest frequency?
(iii) Which class has the highest frequency?
(iv) Which two classes have the same frequency?
| Class interval (Dailv income in rupees) | Frequency (Number of workers) |
|---|---|
| 200-225 | 25 |
| 225-250 | 38 |
| 250-275 | 42 |
| 275-300 | 45 |
| 300-325 | 17 |
| 325-350 | 23 |
| 350-375 | 45 |
| 375-400 | 120 |
| Total | 365 |
(v) What is the lower limit of the class interval 300-325?
(vi) What is the upper limit of the class interval 275-300?
2.
Given below are the marks obtained by 30 students of a class in a test
10, 8, 12, 17, 19, 17, 41, 40, 12, 46, 37, 17, 1, 9, 21, ]3, 48, 12, 21, 19, 33, 5, 38, 39, 19, 23, 2, 6, 30, 27.
Using tally marks prepare a frequency table such that 20-30 is a class interval.
3.
The marks obtained (out of 20) by 30 students of a class in a test are as follows:
14, 16, 15, 11, 15, 14, 13, 16, 8, 10, 7, 11, 18, 15, 14, 19, 20, 7, 10, 13, 12, 14, 15, 13, 16, 17, 14, 11, 10, 20
Prepare a frequency distribution table for the above data using class intervals of equal width in which one class interval is 4-8 (excluding 8 and including 4).
4.
For which of these would you use a histogram to show the data?
(a) The number of letters for different areas in a postman's bag.
(b) The height of competitors in an athletics meet.
(c) The number of cassettes produced by 5 companies.
(d) The number of passengers boarding trains from 7: 00 am to 7: 00 pm at a station.
Give reasons for each.
5.
Consider the histogram given below:
From the bars of this histogram, answer the following questions:
(i) How many teachers are of age 45 yr or more but less than 50 yr?
(ii) How many teachers are of age less than 35 yr?
6.
Percentage wins in ODI by 8 top cricket teams.
| Teams | From champions trophy to world cup 2006 |
Last 10 001 in 2007 |
| South Africa | 75% |
78% |
| Australia | 61% | 40% |
| Sri Lanka | 54% | 38% |
| New Zealand | 47% | 50% |
| England | 46% | 50% |
| Pakistan | 45% | 44% |
| West Indies | 44% | 30% |
| India | 43% | 56% |
7.
Suppose you spin the wheel.
.png)
Find the probability of getting a green sector.
8.
Suppose you spin the wheel.
List the number of outcomes of getting a green sector and not getting a green sector on this wheel (in the above figure).
9.
Represent the following data with the help of a pie diagram.
| Items | Wheat | Rice | Tea |
| Production (in metric tonnes) | 1840 | 3260 | 900 |
10.
The daily income of a group of a factory workers
| Daily income (in Rs) | Number of workers in a factory |
| 75 - 100 | 45 |
| 100 - 125 | 35 |
| 125 - 150 | 55 |
| 150 - 175 | 30 |
| 175 - 200 | 50 |
| 200 - 225 | 125 |
| 225 - 250 | 140 |
| Total | 480 |
11.
Following numbers related to the weekly wages (in Rs) of 18 workers in a factory :
300, 200, 150, 350, 200, 300, 350, 150, 200, 350, 150, 300, 350, 250, 250, 200, 300, 350
Prepare frequency table.
(i) What is the range in wages (in Rs)?
(ii) How many workers are getting Rs 200?
(iii) How many workers are getting the minimum wages?
12.
The difference between the highest and the lowest values of observations in a data is called:
mean of the data
range of the data
total frequency of data
sum of the observations
13.
The class-mark of the class 20-30 is:
20
30
25
10
14.
The range of the data: 6, 14,20, 16,6,5,4, 18,25, 15 and 5 is
4
21
25
20
15.
Monthly salary of a person is Rs 45000. The central angle of the sector representing his expenses on food and house rent on a pie chart is 60°. The amount he spends on food and house rent is
Rs 7500
Rs 4500
Rs 2500
Rs 6000
16.
Which of the following is not a random experiment?
Tossing a coin
Rolling a die
Choosing a card from a deck of 52 cards
Throwing a stone from a roof of a building
17.
Histogram bars are drawn with equal ___________ to a class interval without leaving any gap in between.
18.
The total number of outcomes, when a die is 'thrown, is _____________.
19.
The class size of the interval 28 - 32 is ____________.
20.
The large number of observations are usually organised in groups of equal width called _______.
21.
In a __________ experiment, the outcomes can not be predicted exactly in advance.
22.
The frequency of less than 18 marks is 20.
23.
The frequency of more than 18 marks is 21.
24.
11 students got full marks.
25.
In the class intervals 10 - 20, 20 - 30, etc .... respectively, 20 lies in the class interval 10 - 20.
26.
In a pie chart, a whole circle is divided into sectors.
27.
A bag contains 3 blue and 2 red balls. A ball is drawn at random. What is the probability of drawing a red ball?
28.
A die is thrown once. What is the probability of getting a prime-number?
29.
A die has six faces having dots, 1, 2, 3, 4, 5 and 6 respectively. What is the sum of dots on two faces of a die?
1.
(i) The class interval = [Upper limit of a class] - [Lower limit of the same class] = 225 - 200 = 25
(ii) The class 300 - 325 is having the lowest frequency (which is 17).
(iii) The class 375 - 400 is having the highest frequency (which is 120).
(iv) The class intervals 275-300 and 350 - 375 have the same frequency (which is 45).
(v) The lower limit of the class interval 300 - 325 is 300.
(vi) The upper limit of the class interval 275 - 300 is 300.
2.
The lowest observation = 1
The highest observation = 48
∴ We have
| Marks | Tally marks | Number of students |
|---|---|---|
| 0-10 | |||| | | 6 |
| 10-20 | IIII IIII I | 11 |
| 20-30 | IIII | 4 |
| 30-40 | IIII | 5 |
| 40-50 | IIII | 4 |
3.
| Class interval | Tally marks | Frequency |
| 4 - 8 | II | 2 |
| 8 - 12 | III II | 7 |
| 12 - 16 | III III III | 13 |
| 16 - 20 | III I | 6 |
| 20 - 24 | II | 2 |
| Total | 30 |
4.
We know that, if given data can be grouped into class interval, then we represent the data by histogram. Here, different areas and five companies cannot be grouped into class interval, whereas height and time can be grouped into class interval, so (b) and (d) can be represented by a histogram.
5.
(i) From the above histogram, it is clear that the number of teachers of age 45 yr or more but less than 50 yr are 5.
(ii) Teachers of age less than 35 yr = 4 + 5 + 6 = 15.
6.
Here, comparison between percentage wins in ODI by 8 top cricket teams is given, so to represent the given information, we draw the double bar graph. So, draw two perpendicular axes OX and OY. Take teams on OX and percentage wins in ODI on OY Choose a suitable scale for OX and OY to draw double'bar graph.
Thus, we get the following double bar graph:
7.
Total number of outcomes = Total number of green and red sectors = 5 + 3 = 8
Number of outcomes of getting a green sector = 5
Probability of getting a green sector = \(\frac{Number\ of\ outcomes\ of\ getting\ a\ green\ sector}{Total\ number\ of\ outcomes}=\frac{5}{8}\)
8.
On the wheel, there are three sectors of red colour and five sectors of green colour.
Number of outcomes of getting a green sector on this wheel = 5
Number of outcomes of not getting a green sector on this wheel
Number of outcomes of getting a red sector on this wheel = 3.
9.
.png)
10.
To display the daily income of a group of a factory worker, histogram is more appropriate, since data is given in grouped i.e. intervals.
11.
Frequency table
| Weekly wages (in Rs) | 150 | 200 | 250 | 300 | 350 |
| Number of workers | 3 | 4 | 2 | 4 | 5 |
(i) Rs 200
(ii) 4
(iii) 3.
12.
(b)
range of the data
13.
(c)
25
14.
(b)
21
15.
(a)
Rs 7500
16.
(d)
Throwing a stone from a roof of a building
17.
In a histogram, each class interval has equal width and there is no gap in between the bars.
18.
6 outcomes are 1, 2, 3, 4, 5 and 6.
19.
Upper limit - Lower limit = 32 - 28 = 4
20.
For large number of observations, groups of equal width i.e. class interval are organised.
21.
( )
Random
22.
(b)
23.
(a)
24.
(a)
25.
(b)
26.
(a)
27.
( )
2/5
28.
( )
1/2
29.
( )
7
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