Statistics - Graphical Representation of Data - NCERT Solutions

Steps to draw the histogram:

1. Represent the weights on the horizontal axis with a suitable scale (e.g., 1 cm = 5 kg).
2. Represent the number of students (frequency) on the vertical axis.
3. Draw rectangles with widths equal to the class size and lengths according to the frequencies.

Since there are no gaps between consecutive rectangles, the resultant graph appears like a solid figure. This is called a histogram.

When class widths vary, we need to adjust the lengths of rectangles so that areas are proportional to frequencies.

Steps:

1. Select the class interval with the minimum class size (here, 10).
2. Modify the lengths of rectangles to be proportionate to class-size 10.

To create a frequency polygon from a histogram:

1. Join the mid-points of the upper sides of adjacent rectangles with line segments.
2. Assume a class interval with frequency zero before the first class and after the last class.
3. Join the mid-points of these imaginary classes to complete the polygon.

Steps:

1. Find class marks: \(\text{Class-mark} = \frac{\text{Upper limit + Lower limit}}{2}\)
2. Plot points with class marks on x-axis and frequencies on y-axis.
3. Join these points with line segments.
4. Include points for imaginary classes before the first class and after the last class with zero frequency.

Solution:

First, calculate class marks:

Plot points: (145, 5), (155, 10), (165, 20), (175, 9), (185, 6), (195, 2)

Add points for imaginary classes: (135, 0) and (205, 0)

Join all points to form the frequency polygon.

(i) Graphical representation: A bar graph would be suitable for this data.

(ii) Major cause: Reproductive health conditions (31.8%) is the major cause of women's ill health and death worldwide.

(iii) Factors: With the help of your teacher, identify two major factors contributing to reproductive health conditions being the major cause.

(i) Bar graph representation:

(ii) Conclusions: In the classroom, discuss what conclusions can be arrived at from the graph, such as which sections have higher/lower ratios of girls to boys.

(i) Bar graph:

(ii) Maximum seats: Political Party A won the maximum number of seats (75).

(i) Histogram: First make class intervals continuous by adjusting boundaries.

(ii) Other representation: A frequency polygon would also be suitable for this data.

(iii) Conclusion: No, it is not correct to conclude that the maximum number of leaves are 153 mm long. The class 145-153 has the highest frequency (12 leaves), but this means the leaves in this class have lengths between 145 mm and 153 mm, not exactly 153 mm.

(i) Histogram:

(ii) Lamps with more than 700 hours: 74 + 62 + 48 = 184 lamps have a lifetime of more than 700 hours.

Frequency polygons for both sections:

Comparison: From the polygons, we can compare the performance of both sections. Section B has more students in lower mark ranges (0-20), while Section A has more students in higher mark ranges (20-50).

Frequency polygons for both teams: First make class intervals continuous, then plot frequency polygons for both teams on the same graph.

Histogram: Note that class widths vary, so adjust rectangle heights accordingly.

Histogram: Note that class widths vary, so adjust rectangle heights accordingly.

Class interval with maximum surnames: 6-8 letters (44 surnames).