CBSE Class 8 Mathematics Introduction to Graphs Assignment Set 09

VIII - Mathematics Assignment No - 03 - Introduction to graph

Question 1. The following data gives the marks scored by 120 students in an examination. Represent the data in the form of histogram.
 

Answer:
To represent the given continuous frequency distribution as a histogram, we take Marks along the horizontal axis (X-axis) on a suitable scale and Number of Students along the vertical axis (Y-axis) on a suitable scale. Since the intervals start from 10 instead of 0, a kink (or break mark, \(\text{--}\sim\text{--}\)) is used on the X-axis between 0 and 10.
In simple words: A histogram consists of contiguous rectangular bars where the area of each bar is proportional to the frequency of the class interval.

Exam Tip: Always check if class intervals are continuous before plotting a histogram. Include a break mark (kink) on the axis if values do not start from zero.

Question 2. Construct a histogram for the following data.
 

Answer:
The given class intervals are continuous and start from 40. We represent Marks along the X-axis and Number of Students along the Y-axis. Using a kink between 0 and 40 on the X-axis, we construct adjacent rectangles for each frequency.
In simple words: Draw rectangular bars touching each other without any gaps for each class interval based on its given frequency.

Exam Tip: Ensure bar widths are uniform and proportional to the class size.

Question 3. The following table represent the no. of literate females in the age group 10-44 in a town. Represent the data in the form of histogram.
 

Answer:
Note that the last class interval (35 - 44) has a width of 10, whereas all other preceding intervals have a width of 5. For a correct histogram, we must adjust the heights of the rectangles proportional to a uniform class width (width of 5).
Adjusted frequency for interval 35 - 44 = \(\frac{\text{Given Frequency}}{\text{Class Width}} \times \text{Minimum Class Width} = \frac{6}{10} \times 5 = 3\).
Now, plot the adjusted frequencies against the respective age groups on the histogram.
In simple words: When class intervals are unequal, adjust the heights of the bars by dividing the frequency by the class width.

Exam Tip: Always verify if class intervals are of equal width before drawing a histogram. Adjust frequencies if widths vary.

Question 4. The distribution of heights (in cm) of 100 people is given below. Draw its histogram.
 

Answer:
The class intervals are continuous with a uniform width of 10. We represent Heights on the X-axis and Number of people on the Y-axis. Using a kink between 0 and 145 on the X-axis, we plot the bars.
In simple words: Plot the height intervals on the X-axis and frequencies on the Y-axis using continuous bars.

Exam Tip: Label both axes clearly with units (cm for height and number of people for frequency).