GSEB Class 8 Maths Solutions Chapter 5 Data Handling Exercise 5.1

Question 1. 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 a.m. to 7:00 p.m. at a station.
Give reasons for each?
Answer: We show that data using a histogram if it can be put into class intervals. Clearly, for (b) and (d), histograms are suitable for presenting the information. Option (a) involves discrete categories (different areas), and option (c) also involves discrete categories (5 companies), which are better suited for bar graphs.
In simple words: Histograms are for data that can be put into groups or ranges, like height ranges or time slots. Options (b) and (d) fit this, so they are good for histograms. Options (a) and (c) are for separate categories, so bar graphs would be better.

Exam Tip: Histograms are useful for continuous data (like height or time) that can be grouped into intervals, where the bars touch. Bar graphs are for categorical or discrete data, where the bars are separate.

Question 2. The shoppers who come to a departmental store are marked as: man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning:
WWWGBWWMGGMMWWWWGBMWBGGMWWMMWW
WMWBWGM WWWWGWMMWWMWGWMGWMMBGGW
Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.
Answer:
The frequency distribution table for the given data can be:

Exam Tip: For categorical data like types of shoppers, a frequency distribution table and a bar graph are the correct ways to display the information. Ensure tally marks are counted accurately, with each group of five indicated by a diagonal slash.

Question 3. 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.
Answer:
The smallest wage found is 804.
The largest wage is 898.
The specific groups are: 800-810, 810-820, etc.
The frequency distribution table is:

Exam Tip: When creating class intervals, ensure they are continuous (e.g., 800-810, 810-820) and cover all data points from the lowest to the highest observation. The upper limit of one interval (e.g., 810 in 800-810) is typically excluded from that interval and included in the next (810-820).

Question 4. Draw a histogram for the frequency table made for the data in Question 3, and answer the following questions?
1. Which group has the maximum number of workers?
2. How many workers earn ₹ 850 and more?
3. How many workers earn less than ₹ 850?
Answer:
The histogram for the frequency table created earlier is shown. In this graph, we have placed the class intervals on the horizontal line, and the number of workers (frequencies) are displayed along the vertical line.
Now, we can answer the questions:
1. The group with wages between 830 and 840 contains the highest number of workers.
2. The number of workers earning Rs. 850 or more is found by adding: \( 1 + 3 + 1 + 1 + 4 = 10 \).
3. The count of workers earning less than Rs. 850 is calculated as: \( 3 + 2 + 1 + 9 + 5 = 20 \).
In simple words: To make the histogram, put the wage groups on the bottom and the number of workers on the side. The bars should touch because the groups are continuous. Then, use the graph to find the answers: which bar is tallest, and how many workers are in the groups that are Rs. 850 or more, or less than Rs. 850.

Exam Tip: A histogram is used for continuous data, where bars touch to show continuity. Carefully read the graph to answer questions about frequencies within specified ranges. Remember to include the lower bound of an interval when summing for "or more" and exclude the upper bound for "less than."

Question 5. The number of hours for which students of a particular class watched television during holidays is shown through the given graph. Answer the following.
1. For how many hours the maximum number of students watched TV?
2. How many students watched TV for less than 4 hours?
3. How many students spent more than 5 hours in watching TV?
Answer:
The graph for the number of hours students watched television is given below:
1. The duration for which the highest number of students watched television is 4 to 5 hours.
2. The total count of students who watched TV for less than 4 hours is \( 4 + 8 + 22 = 34 \).
3. The total number of students who spent more than 5 hours watching TV is \( 8 + 6 = 14 \).
In simple words: Look at the graph. Find the tallest bar to see when most students watched TV. For less than 4 hours, add up the student counts for the 1-2, 2-3, and 3-4 hour groups. For more than 5 hours, add up the student counts for the 5-6 and 6-7 hour groups.

Exam Tip: When answering questions based on a graph, pay close attention to the labels on both axes and the ranges defined for each bar to ensure accurate data extraction and calculation. For questions involving ranges (e.g., "less than 4 hours"), sum the frequencies of all relevant preceding intervals.