RD Sharma Class 8 Solutions Chapter 24 Free PDF
FAQs on RD Sharma Class 8 Solutions Chapter 24 - Graphical Representation of Data As Histograms (Ex 24.2) Exercise 24.2
1. What is the main difference between a bar graph and a histogram when solving data representation problems in Class 8?
The primary difference lies in the type of data they represent. A bar graph is used for discrete, separate categories (e.g., favourite colours, number of students in different houses), with distinct gaps between the bars. In contrast, a histogram is used to represent continuous data that is grouped into ranges or class intervals (e.g., marks of students, heights of people). The bars in a histogram touch each other to show that the data is continuous.
2. What are the essential steps to correctly construct a histogram for the problems in RD Sharma Class 8, Ex 24.2?
To correctly construct a histogram as per the problems in this exercise, you should follow these steps:
Step 1: Create a frequency distribution table from the given data. If class intervals are not continuous (e.g., 1-10, 11-20), adjust them to be continuous (e.g., 0.5-10.5, 10.5-20.5).
Step 2: Draw two perpendicular axes – the horizontal x-axis for class intervals and the vertical y-axis for frequencies.
Step 3: Choose an appropriate scale for both axes.
Step 4: Mark the class intervals on the x-axis.
Step 5: Draw rectangular bars with widths equal to the class size and heights corresponding to the frequencies. Ensure there are no gaps between consecutive bars.
3. Why are the bars in a histogram drawn without any gaps, and what does this signify about the data?
The bars in a histogram are drawn without any gaps to signify that the data being represented is continuous. This means that the upper limit of one class interval is the same as the lower limit of the next class interval. The absence of gaps visually represents that there are no breaks in the data ranges, and the data flows from one interval to the next without interruption.
4. How do you create a frequency distribution table from raw data before drawing a histogram?
To create a frequency distribution table from a set of raw data, you first need to decide the class intervals. Group the data into these intervals and then count the number of data points that fall into each interval. This count is the frequency for that class. It is common to use tally marks to keep track of the count for each interval before writing the final frequency.
5. If a question in RD Sharma gives class intervals like 5-9, 10-14, 15-19, what adjustment is required before drawing the histogram?
When class intervals are discontinuous like 5-9 and 10-14, you must make them continuous. To do this, find the gap between the upper limit of one class (9) and the lower limit of the next class (10). The gap is 1. The adjustment factor is half of this gap, which is 0.5. You must subtract 0.5 from all lower limits and add 0.5 to all upper limits. The new, continuous intervals would be 4.5-9.5, 9.5-14.5, 14.5-19.5, and so on. This is a mandatory step before plotting the histogram.
6. How does a histogram help in understanding the distribution of data from a frequency table?
A histogram provides a quick visual summary of data distribution. By looking at the graph, you can instantly identify:
The shape of the data (e.g., symmetric, skewed).
The modal class, which is the class interval with the highest frequency, represented by the tallest bar.
The spread or dispersion of the data across the different intervals.
Any potential outliers or gaps in the data set.
7. What information is represented on the horizontal (x-axis) and vertical (y-axis) of a histogram?
In a histogram, the horizontal axis (x-axis) is used to represent the continuous data in the form of class intervals. The vertical axis (y-axis) represents the frequency of the data, which is the count of observations falling within each class interval. The height of each bar corresponds to the frequency of that specific interval.
