CBSE Class 8 Maths Chapter 5 Data Handling NCERT Solutions

A histogram is a graphical representation of data that is grouped into class intervals. It is best suited for showing the distribution of continuous numerical data.

Let's analyze each option:

1. The number of letters for different areas in a postman's bag: This data is likely categorical (areas) or discrete counts for each area. A bar graph would be more appropriate to compare the number of letters for different areas.
2. The height of competitors in an athletics meet: Heights are continuous numerical data. Competitors' heights can be grouped into intervals (e.g., 150-155 cm, 155-160 cm). Therefore, a histogram is suitable for showing the distribution of heights.
3. The number of cassettes produced by 5 companies: This data involves comparing discrete values (number of cassettes) for different companies. A bar graph is the appropriate choice here.
4. The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station: This data represents the number of passengers over time intervals (e.g., hourly). Since time can be divided into continuous intervals and we are looking at frequencies within these intervals, a histogram is suitable.

Reasoning: Histograms are used when the data is continuous and can be divided into class intervals. Options (b) and (d) involve data that fits this description, allowing for the visualization of frequency distributions over ranges.

First, we count the occurrences of each category of shopper using tally marks to create a frequency distribution table.

Frequency Distribution Table:

Note: The source text had some inconsistencies in the tally marks and counts for 'M' and 'G'. The table above reflects the correct count from the provided list of shoppers.

Bar Graph Illustration:

To draw the bar graph, we take the shopper types on the x-axis and the number of shoppers (frequency) on the y-axis. Each category will have a bar whose height corresponds to its frequency.

(Note: A visual bar graph cannot be generated in this text-based format. However, the description below explains how to construct it.)

Steps to draw the bar graph:

1. Draw two perpendicular lines: the horizontal axis (x-axis) and the vertical axis (y-axis).
2. Label the x-axis as 'Shopper Type' and mark 'W', 'M', 'B', 'G' at equal intervals.
3. Label the y-axis as 'Number of Shoppers'. Choose a suitable scale. Since the frequencies range from 5 to 28, a scale like 1 unit = 2 shoppers or 1 unit = 5 shoppers would be appropriate. Mark the scale values (e.g., 0, 5, 10, 15, 20, 25, 30) along the y-axis.
4. Draw rectangular bars for each shopper type. The width of each bar should be uniform, and there should be a gap between consecutive bars.
5. The height of the bar for 'W' should reach 28 on the y-axis.
6. The height of the bar for 'M' should reach 13 on the y-axis.
7. The height of the bar for 'B' should reach 5 on the y-axis.
8. The height of the bar for 'G' should reach 7 on the y-axis.
9. Add a title to the graph, such as 'Shoppers in a Departmental Store during the First Hour'.

We need to organize the given weekly wages into a frequency table using specified class intervals. The intervals are given as 800-810, 810-820, and so on. We will use tally marks to count the number of workers falling into each interval.

Frequency Table of Weekly Wages:

Note: The sum of frequencies is 36, which differs from the stated 30 workers. Let's re-verify the counts based on the provided list and intervals.

Re-calculation based on 30 workers:

Let's carefully list the wages and assign them to intervals:

• 800-810: 804, 808, 806 (3 workers)
• 810-820: 810, 812 (2 workers)
• 820-830: 820 (1 worker)
• 830-840: 830, 835, 835, 836, 832, 833, 835, 835, 836 (9 workers)
• 840-850: 845, 845, 840, 840, 840 (5 workers)
• 850-860: 855 (1 worker)
• 860-870: 869, 860, 868 (3 workers)
• 870-880: 878 (1 worker)
• 880-890: 885 (1 worker)
• 890-900: 890, 898, 890, 890 (4 workers)

Corrected Frequency Table:

Note on Intervals: Conventionally, in intervals like 800-810, the lower limit (800) is included, and the upper limit (810) is excluded. However, if a value falls exactly on the upper limit of one interval and the lower limit of the next (e.g., 810), it is typically placed in the interval where it is the lower limit. The corrected table follows this convention, placing 810 in 810-820, 820 in 820-830, and so on. The source text's table had significant errors in counts and interval representation.