Welcome to AssamSchool. This article contains 30 Extra Questions from Statistics from Class 9 Mathematics Chapter 12. These Statistics Class 9 Extra Questions are helpful to test your understanding and knowledge of the chapter. These additional questions will not only help you to excel in the chapter but also will give you a strong foundation in Mathematics.
We have also provided step-by-step answers to the questions for reference. So, let’s start…
30 Statistics Class 9 Extra Questions
1. In a bar graph, what does the height of each bar represent?
2. True or False: In a histogram, the width of each bar corresponds to the class interval’s range.
3. The following data shows the number of students in different weight categories (in kg):
\(
\begin{array}{|c|c|}
\hline
\text{Weight Categories} & \text{Number of Students} \\ \hline
30.5-35.5 & 9 \\
35.5-40.5 & 6 \\
40.5-45.5 & 15 \\
\hline
\end{array}
\)
Draw a histogram for this data.
4. Calculate the class mark for the interval \(140-150\).
5. A histogram for the marks of 90 students has varying class widths. The intervals and frequencies are:
\(
\begin{array}{|c|c|}
\hline
0-20 & 7 \\
20-30 & 10 \\
30-40 & 10 \\
\hline
\end{array}
\)
Adjust the histogram to ensure areas are proportional to frequencies.
6. The frequency polygon for a dataset requires plotting midpoints. If the class intervals are 10-20, 20-30, etc., what are the midpoints?
7. In Example 1 (birth months), which month had the least number of students born?
8. What is the purpose of a “kink” on the horizontal axis in a histogram?
9. Convert the discontinuous class intervals 118-126, 127-135, etc., into continuous intervals and draw a histogram.
10. A bar graph shows the expenditure (in ₹1000s) of a family:
\(
\begin{array}{|c|c|}
\hline
\text{Grocery} & 4 \\
\text{Rent} & 5 \\
\text{Education} & 5 \\
\hline
\end{array}
\)
If the scale is 1 unit = ₹1000, what is the height of the “Education” bar?
11. Two sections of students have marks distributed as follows:
\(
\begin{array}{|c|c|c|}
\hline
\text{Marks} & \text{Section A} & \text{Section B} \\
\hline
0-10 & 3 & 5 \\
10-20 & 9 & 19 \\
\hline
\end{array}
\)
Plot frequency polygons for both sections on the same graph and compare performance.
12. What is the formula for calculating the class mark of an interval?
13. A frequency distribution table has intervals 140-150, 150-160, etc. Compute the class marks.
14. A histogram with intervals 70-100 (frequency 8) and 60-70 (frequency 15) is misleading. Correct it using proportionate lengths.
15. True or False: A frequency polygon must always start and end at zero frequency.
16. For the following data, draw a frequency polygon without constructing a histogram:
\(
\begin{array}{|c|c|}
\hline
\text{Cost of living index} & \text{Number of weeks} \\
\hline
140-150 & 5 \\
150-160 & 10 \\
\hline
\end{array}
\)
17. The lifetime of neon lamps is given as:
\(
\begin{array}{|c|c|}
\hline
300-400 & 14 \\
400-500 & 56 \\
\hline
\end{array}
\)
Represent this data in a histogram and calculate how many lamps lasted more than 700 hours.
18. In a bar graph, what is the gap between bars used for?
19. The following table shows surnames by letter count:
\(
\begin{array}{|c|c|}
\hline
1-4 & 6 \\
4-6 & 30 \\
\hline
\end{array}
\)
Convert to continuous intervals and draw a histogram.
20. A survey shows women’s fatality causes: Reproductive health (31.8%), Injuries (12.4%). Represent this data in a bar graph and identify the major cause.
21. What graphical form is suitable for comparing two datasets?
22. For age groups 1-2, 2-3, etc., with frequencies 5, 3, etc., explain why a histogram is appropriate.
23. A frequency polygon for marks 0-10, 10-20, etc., requires extending the graph. How would you plot the pre-zero class?
24. If a class interval is 30.5-35.5, what is its width?
25. Adjust the histogram for the interval 70-100 (width 30, frequency 8) to match a class size of 10.
26. A dataset has intervals 0-20, 20-30, with frequencies 7 and 10. Compute the adjusted bar heights for a histogram.
27. In a frequency polygon, what do the plotted points represent?
28. Given class marks 145, 155, etc., and frequencies 5, 10, etc., plot the frequency polygon.
29. The runs scored by Team A and B in a cricket match are given. Represent both as frequency polygons on the same graph.
30. True or False: A histogram can have gaps between bars.
Answers
- Solution:
The height represents the frequency or value of the variable. - Solution:
True. - Solution:
Draw bars with widths 5 kg (30.5-35.5, etc.) and heights corresponding to frequencies (9, 6, 15). - Solution:
Class mark = \(\frac{140 + 150}{2} = 145\) - Solution:
Adjust lengths:
For 0-20: \(\frac{7}{20} \times 10 = 3.5\) units.
For 20-30: \(\frac{10}{10} \times 10 = 10\) units. - Solution:
Midpoints: 15, 25, 35, etc. - Solution:
November (4 students). - Solution:
To indicate a break when the axis does not start at zero. - Solution:
Convert to 117.5-126.5, 126.5-135.5, etc., then draw the histogram. - Solution:
Height = 5 units (since ₹5000 ÷ ₹1000 = 5) - Solution:
Plot midpoints (5, 15, etc.) for both sections and connect lines. Section B performs worse in lower intervals. - Solution:
\(\frac{\text{Upper limit + Lower limit}}{2}\) - Solution:
145, 155, 165, 175, 185, 195. - Solution:
Adjusted length for 70-100: \(\frac{8}{30} \times 10 = 2.67\) units. - Solution:
True (to form a closed shape). - Solution:
Plot class marks 145 (5), 155 (10), etc., and connect the points. - Solution:
Lamps >700 hours: 74 + 62 + 48 = 184. - Solution:
For clarity and visual separation between categories. - Solution:
Convert to 0.5-4.5, 4.5-6.5, etc., then draw bars. - Solution:
Reproductive health (31.8%) is the major cause. - Solution:
Frequency polygon or dual bar graph. - Solution:
Histograms are used for continuous data with grouped intervals. - Solution:
Extend the horizontal axis to include an imaginary class (-10)-0 with midpoint -5 and frequency 0. - Solution:
Width = 35.5 – 30.5 = 5 kg. - Solution:
Length = \(\frac{8}{30} \times 10 = 2.67\) units. - Solution:
Adjusted heights: 3.5 and 10 units. - Solution:
Midpoints of classes and their corresponding frequencies. - Solution:
Plot points (145, 5), (155, 10), etc., and connect them. - Solution:
Convert intervals to continuous (0.5-6.5, etc.), find midpoints, and plot both polygons. - Solution:
False. Histograms have no gaps between bars.
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The Bottom Line
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Abdur Rohman is an Electrical Engineer from Charaideo, Assam, who wears multiple hats as a part-time teacher, blogger, entrepreneur, and digital marketer. Passionate about education, he founded The Assam School blog to provide free, comprehensive textbook solutions, MCQs (Multiple Choice Questions), and other academic content for students from Class V to XII.