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Page No 234:
Question 1:
The number of members in 20 families are given below:
4, 6, 5, 5, 4, 6, 3, 3, 5, 5, 3, 5, 4, 4, 6, 7, 3, 5, 5, 7.
Prepare a frequency distribution of the data.
Answer:
First, we will arrange the data in increasing order.
3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7
Frequency table of the above data:
| Number of members | Tally marks | Number of families (frequency) |
| 3 | 4 | |
| 4 | 4 | |
| 5 | 7 | |
| 6 | 3 | |
| 7 | 2 | |
| Total | 20 |
Page No 234:
Question 2:
A dice was thrown 30 times and the following outcomes were noted:
2, 1, 2, 4, 6, 1, 2, 3, 6, 5, 4, 4, 3, 1, 1, 3, 1, 1, 5, 6, 6, 2, 2, 3, 4, 2, 5, 5, 6, 4.
Prepare a frequency table.
Answer:
Arranging the outcomes in increasing order, we get:
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6
Now, we have:
1 was thrown 6 times
2 was thrown 6 times
3 was thrown 4 times
4 was thrown 5 times
5 was thrown 4 times
6 was thrown 5 times
Frequency distribution table of the above data:
| Number | Tally mark | frequency |
| 1 | 6 | |
| 2 | 6 | |
| 3 | 4 | |
| 4 | 5 | |
| 5 | 4 | |
| 6 | 5 | |
| Total | 30 |
Page No 234:
Question 3:
The 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, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.
Represent it in the form of a frequency distribution.
Answer:
Arranging the dates in ascending order, we get:
0, 0 ,0 , 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,2,2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6
There are:
4 families with no children
7 families with 1 child
12 families with 2 children
5 families with 3 children
6 families with 4 children
3 families with 5 children
3 families with 6 children
The frequency distribution table for the above data can be generated as below:
| Number of children | Tally mark | Number of families (frequency) |
| 0 | 4 | |
| 1 | 7 | |
| 2 | 12 | |
| 3 | 5 | |
| 4 | 6 | |
| 5 | 3 | |
| 6 | 3 | |
| Total | 40 |
Page No 235:
Question 1:
The marks obtained by 40 students of a class in an examination are given below:
8, 47, 22, 31, 17, 13, 38, 26, 3, 34, 29, 11, 22, 7, 15, 24, 38, 31, 21, 35, 42, 24, 45, 23, 21, 27, 29, 49, 25, 48, 21, 15, 18, 27, 19, 45, 14, 34, 37, 34.
Prepare a frequency distribution table with equal class intervals, starting from 0−10 (where 10 not included).
Answer:
Arranging the given observations in ascending order, we get:
3, 7, 8, 11, 13, 14, 15, 15, 17, 18, 19, 21, 21, 21, 22, 22, 23, 24, 24, 25, 26, 27, 27, 29, 29, 31, 31, 34, 34, 34, 35, 37, 38, 38, 42, 45, 45, 47, 48, 49
Thus, the frequency distribution may be represented as shown below:
| Marks | Tally marks | Frequency |
|---|---|---|
| 0-10 | ||| | 3 |
| 10-20 | 8 | |
| 20-30 | 14 | |
| 30-40 | 9 | |
| 40-50 | 6 | |
| Total | 40 |
Page No 235:
Question 2:
The electricity bills (in rupees) of 25 houses of a certain locality for a month are given below:
324, 700, 617, 400, 356, 365, 435, 506, 548, 736, 780, 378, 570, 685, 312, 630, 584, 674, 754, 776, 596, 745, 565, 763, 472.
Arrange the above data in increasing order and form a frequency table using equal class intervals, starting from 300−400, where 400 is not included.
Answer:
Arranging the given observations in increasing order, we get:
312, 324, 356, 365, 378, 400, 435, 472, 506, 548, 565, 570, 584, 596, 617, 630, 674, 685, 700, 736, 745, 754, 763, 776, 786
Thus, the frequency distribution may be represented as shown below:
| Electricity bills (in Rupees) |
Tally marks | Frequency |
|---|---|---|
| 300-400 | 5 | |
| 400-500 | ||| | 3 |
| 500-600 | 6 | |
| 600-700 | |||| | 4 |
| 700-800 | 7 | |
| Total | 25 |
Page No 235:
Question 3:
The weekly wages (in rupees) of 28 workers of a factory are given below:
668, 610, 642, 658, 668, 620, 719, 720, 700, 690, 710, 642, 672, 654, 692, 706, 718, 702, 704, 678, 615, 640, 680, 716, 705, 615, 636, 656.
Construct a frequency table with equal class intervals, taking the first of the class intervals as 610−630, where 630 is not included.
Answer:
Arranging the given observations in ascending order, we get:
610, 615, 615, 620, 636, 640, 642, 642, 654, 656, 658, 668, 668, 672, 678, 680, 690, 692, 700, 702, 704, 705, 706, 710, 716, 718, 719, 720
Thus, the frequency distribution may be represented as shown below:
| Weekly wages (in Rupees) |
Tally marks | Frequency |
|---|---|---|
| 610-630 | |||| | 4 |
| 630-650 | |||| | 4 |
| 650-670 | 5 | |
| 670-690 | ||| | 3 |
| 690-710 | 7 | |
| 710-730 | 5 | |
| Total | 28 |
Page No 235:
Question 4:
The weekly pocket expenses (in rupees) of 30 students of a class are given below:
62, 80, 110, 75, 84, 73, 60, 62, 100, 87, 78, 94, 117, 86, 65, 68, 90, 80, 118, 72, 95, 72, 103, 96, 64, 94, 87, 85, 105, 115.
Construct a frequency table with class intervals 60−70 (where 70 is not included), 70−80, 80−90, etc.
Answer:
Arranging the given observations in increasing order, we get:
60, 62, 62, 64, 65, 68, 72, 72, 73, 75, 78, 80, 80, 84, 85, 86, 87, 87, 90, 94, 94, 95, 96, 100, 103, 105, 110, 115, 117, 118
Thus, the frequency distribution may be represented as given below:
| Weekly pocket expenses (in Rupees) |
Tally marks | Frequency |
|---|---|---|
| 60-70 | 6 | |
| 70-80 | 5 | |
| 80-90 | 7 | |
| 90-100 | 5 | |
| 100-110 | ||| | 3 |
| 110-120 | |||| | 4 |
| Total | 30 |
Page No 236:
Question 5:
The daily earnings (in rupees) of 24 stores in a market was recorded as under:
715, 650, 685, 550, 573, 530, 610, 525, 742, 680, 736, 524, 500, 585, 723, 545, 532, 560, 580, 545, 625, 630, 645, 700.
Prepare a frequency table taking equal class sizes. One such class is 500−550, where 550 is not included.
Answer:
Arranging the given observations in increasing order, we get:
500, 524, 525, 530, 532, 545, 545, 550, 560, 573, 580, 585, 610, 625, 630, 645, 650, 680, 685, 700, 715, 723, 736, 742
Thus, the frequency distribution may be represented as given below:
| Daily earnings (in Rupees) |
Tally marks | Frequency |
|---|---|---|
| 500-550 | ||||| || | 7 |
| 550-600 | ||||| | 5 |
| 600-650 | |||| | 4 |
| 650-700 | ||| | 3 |
| 700-750 | ||||| | 5 |
| Total | 24 |
Page No 236:
Question 6:
The heights (in cm) of 22 students were recorded as under:
125, 132, 138, 144, 142, 136, 134, 125, 135, 130, 126, 132, 135, 142, 143, 128, 126, 136, 135, 130, 130, 133.
Prepare a frequency distribution table, taking equal class intervals and starting from 125−130, where 130 is not included.
Answer:
Arranging the given observations in increasing order, we get 125, 125, 126, 126, 128, 130, 130, 130, 132, 132, 133, 134, 135, 135, 135, 136, 136, 138, 142, 142, 143 and 144.
Thus, the frequency distribution may be represented as given below:
| Heights (in cm) | Tally marks | Frequency |
|---|---|---|
| 125-130 | 5 | |
| 130-135 | 7 | |
| 135-140 | 6 | |
| 140-145 | |||| | 4 |
| Total | 22 |
Page No 239:
Question 1:
The top speeds of 30 different land animals have been organised into a frequency table given below:
| Maximum speed (in km/h) | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | 60–70 |
| Number of animals | 3 | 5 | 10 | 8 | 0 | 2 |
Draw a histogram for the given data.
Answer:
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Page No 239:
Question 2:
The ages (in years) of 360 patients treated in a hospital on a particular day are given below:
| Age (in years) | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | 60–70 |
| Number of patients | 90 | 40 | 60 | 20 | 120 | 30 |
Draw a histogram for the given data.
Hint. Take 10 small divisions = 10 patients.
Answer:
.png)
Page No 239:
Question 3:
Draw a histogram for the frequency distribution of following data:
| Class interval | 8–13 | 13–18 | 18–23 | 23–28 | 28–33 | 33–38 | 38–43 |
| Frequency | 320 | 780 | 160 | 540 | 260 | 100 | 80 |
Hint. Take 1 small division = 10.
Answer:
(1).png)
Page No 239:
Question 4:
Draw a histogram for the frequency distribution of the following data:
| Class interval | 20–25 | 25–30 | 30–35 | 35–40 | 40–45 | 45–50 |
| Frequency | 30 | 24 | 52 | 28 | 46 | 10 |
Answer:
.png)
Page No 239:
Question 5:
Draw a histogram for the following data:
| Class interval | 600–640 | 640–680 | 680–720 | 720–760 | 760–800 | 800–840 |
| Frequency | 18 | 45 | 153 | 288 | 171 | 63 |
Hint. Take 1 small division = 3.
Answer:
.png)
ans
Page No 240:
Question 6:
The following table shows the number of illiterate persons in the age group (10–58 years) in a town. Represent the given data by means of a histogram.
| Age group (in years) | 10–18 | 18–26 | 26–34 | 34–42 | 42–50 | 50–58 |
| Number of illiterate persons | 175 | 325 | 100 | 150 | 250 | 525 |
Hint. Take 1 small division = 5 persons.
Answer:
.png)
Page No 240:
Question 7:
The marks obtained (out of 20) by 30 students of a class in a test are given below:
7, 10, 8, 16, 13, 14, 15, 11, 18, 11, 15, 10, 7, 14, 20, 19, 15, 16, 14, 20, 10, 11, 14, 17, 13, 12, 15, 14, 16, 17.
Prepare a frequency distribution table for the above data using class intervals of equal width in which one class interval in 3–8 (including 2 and excluding 8). From the frequency distribution table so obtained, draw a histogram.
Answer:
Frequency distribution table
| Marks | Tally Marks | Number of students |
| 3-8 | 2 | |
| 8-13 | 8 | |
| 13-18 | 16 | |
| 18-23 | 4 | |
| Total = | 30 |
(2).png)
Page No 240:
Question 8:
The weights (in kg) of 30 students of a class are
39, 43, 32, 37, 29, 26, 31, 45, 46, 31, 37, 38, 30, 39, 36, 41, 35, 34, 41, 46, 39, 38, 36, 38, 40, 42, 33, 43, 44, 33.
Prepare a frequency distribution table using one class interval as 30–35, in which 30 is included and 35 excluded. Using the above data. draw a histogram.
Answer:
Frequency distriubution table
| Weight(in kg) | Tally Marks | Number of students |
| 25-30 | 2 | |
| 30-35 | 7 | |
| 35-40 | 11 | |
| 40-45 | 7 | |
| 45-50 | 3 | |
| Total = | 30 |
(1).png)
Page No 240:
Question 9:
Look at the histogram given below and answer the question that follow:
(i) How many students have height more than or equal to 135 cm but less than 150 cm?
(ii) Which class interval has the least number of students?
(iii) What is the class size?
(iv) How many students have height less than 140 cm?
Answer:
(i) Number of students =
(ii) Class interval with least number of students = 150−155
(iii) Class size = 130 − 125 = 5
(iv) Number of students with height less than 140 =
Page No 241:
Question 10:
Look at the histogram given below and answer the question that follow:
(i) What information is being given by the histogram?
(ii) How many teachers are of age less than 45 years?
(iii) How many teachers are of age 40 years or more but less than 55 years?
Answer:
(i) The given histogram tells about the number of teachers in a school from the age group 25-30 to 55-60.
(ii) Number of teachers with age less than 45 years =
(iii) Number of teachers with age more than 40 years but less than 55 years =
Page No 241:
Question 11:
The histogram given below shows the number of literate females in the age group of 10 to 40 years. Study the histogram carefully and answer the question that follow:
(i) Write the classes, assuming that all the classes are of equal width.
(ii) What is the class width?
(iii) In which age group are the literate females the least?
(iv) In which age group is the number of literate females the highest?
Hint. Number of class intervals of equal width = 6 (given), class width =
Answer:
(i) Age group =10 to 40
Given all the classes are of equal width
Number of class interval of equal width = 6
Class width =
Classes are 10-15,15-20,20-25,25-30,30-35,35-40
(ii) Class width =
(iii)Age group with least literate females = 10-15
(iv)Age group with highest literate females = 15-20
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