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Maths 5 Mark Question

Data Handling - II (Graphical Representation of Data as Histograms) · Maharashtra Board STD 8 (MSBSHSE - English Medium). 9 questions.

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9 questions · self-marked practice — reveal the answer and mark yourself.

Question 15 Marks
Given below is the frequency distribution of the heights of 50 students of a class:
Class interval
140-145
145-150
150-155
155-160
160-165
Frequency
8
12
18
10
5
Draw a histogram representing the above data.
Answer
The class limits are represented along the x-axis on a suitable scale and the frequencies are represented along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be constructed to obtain the histogram of the given frequency distribution as shown in the figure below:
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Question 25 Marks
Number of workshops organized by a school in different areas during the last five years are as follows:
Year No. of workshops
1995-1996 25
1996-1997 30
1997-1998 42
1998-1999 50
1999-2000 65
Draw a histogram representing the above data.
Answer
The class limits are represented along the x-axis and the frequencies are represented along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be constructed to obtain histogram for the given frequency. The histogram is shown below:
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Question 35 Marks
Draw a histogram for the daily earnings of 30 drug stores in the following table:
Daily earnings (in Rs.)
450-500
500-550
550-600
600-650
650-700
Numbers of stores
16
10
7
3
1
Answer
The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is given below:
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Question 45 Marks
Draw a histogram to represent the following data:
Monthly salary (in Rs.)
Number of teachers
5600-5700
8
5700-5800
4
5800-5900
3
5900-6000
5
6000-6100
2
6100-6200
3
6200-6300
1
6300-6400
2
Answer
Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be constructed to obtain the histogram of the given data. The class intervals are represented along the x-axis and the frequencies along the y-axis on a suitable scale. The histogram representing the given data is shown below:
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Question 55 Marks
Construct a histogram for the following data:
Monthly school fee (in Rs.)
30-60
60-90
90-120
120-150
150-180
180-210
210-240
Number of schools
5
12
14
18
10
9
4
Answer
The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking class intervals as bases and corresponding frequencies as heights of the rectangles, the histogram of the given data can be obtained as shown in the figure below:
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Question 65 Marks
Draw a histogram of the following data:
Class interval:
10-15
15-20
20-25
25-30
30-35
35-40
Frequency:
30
98
80
58
29
50
Answer
The class limits are represented along the x-axis and the frequencies are represented along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is shown below:
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Question 75 Marks
In a hypothetical sample of 20 people the amounts of money with them were found to be as follows:
114, 108, 100, 98, 101, 109, 117, 119, 126, 131, 136, 143, 156, 169, 182, 195, 207, 219, 235, 118.
Draw the histogram of the frequency distribution (taking one of the class intervals as 50-100).
Answer
We first prepare the frequency table for the class intervals 50-100, 100-150, ........., 200-250, as shown below:
Money
Tally Amount
Frequency
50-100
98
1
100-150
114, 108, 100, 101, 109, 117, 119, 126, 131, 136, 143, 118
12
150-200
156, 169, 182, 195
4
200-250
207, 219, 235
3
The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking the class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is shown below:
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Question 85 Marks
The following histogram shows the number of literate females in the age group of 10 to 40 years in a town:
  1. Write the age group in which the number of literate female is the highest.
  2. What is the class width?
  3. What is the lowest frequency?
  4. What are the class marks of the classes?
  5. In which age group literate females are the least?
Answer
The highest rectangle corresponds to the highest number of literate females, which is in the interval 15-20 years.
The class intervals are 10-15, 15-20, 20-25, 30-35, 35-40. Hence, the class width is 5.
The lowest rectangle corresponds to the lowest frequency, which is 320.
The class mark is the mid-point of the class interval.
$\text{Class mark}=\frac{\text{upper limit }+\text{ lower limit}}{2}$
Hence, the class mark of each class is as follows:
Interval
Class Mark
10-15
12.5
15-20
17.5
20-25
22.5
25-30
27.5
30-35
32.5
35-40
37.5
The lowest rectangle corresponds to the least number of literate females, which is in the interval 10-15 years.
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Question 95 Marks
The weekly wages (in Rs.) of 30 workers in a factory are given:
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
Mark a frequency table with intervals as 800-810, 810-820 and so on, using tally marks. Also, draw a histogram and answer the following questions:
  1. Which group has the maximum number of workers?
  2. How many workers earn Rs. 850 and more?
  3. How many workers earn less than Rs. 850?
Answer
The frequency table with intervals 800-820, 810-820, ........., 890-900 is given below:
The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, the rectangles can be drawn to obtain the histogram of the given frequency distribution. The histogram is shown below:
  1. The group that has the maximum number of workers is represented as the highest rectangle. It is in the interval 830-840
  2. The number of workers who earn Rs. 850 or more can be calculated from frequency table in the following manner:
1 + 3 + 1 + 1 + 4 = 10
  1. The number of workers who earn less than Rs. 850 can be calculated from frequency table in the following manner:
3 + 2 + 1 + 9 + 5 = 20
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