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Q9(i):
100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
(i) Draw a histogram to depict the given information.
100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
(i) Draw a histogram to depict the given information.
Solution :
Step 1: Data Organization & Frequency Table
To construct a histogram for continuous data, we represent the classes along the x-axis and the frequencies along the y-axis. Since the class intervals are already provided and are continuous, we can plot them directly.
| Number of letters | Number of surnames (Frequency) |
|---|---|
| 1 - 4 | 6 |
| 4 - 6 | 30 |
| 6 - 8 | 44 |
| 8 - 12 | 16 |
| 12 - 20 | 4 |
Step 2: Adjusted Frequency for Unequal Class Widths
Because the class widths (the difference between upper and lower limits) are not uniform, we must calculate the frequency density to ensure the area of each rectangle is proportional to the frequency. [Per the rule for histograms with varying intervals: $\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}} \times \text{Minimum Class Width}$]. Let the minimum class width be $2$.
| Class Interval | Frequency ($f$) | Width ($h$) | Adjusted Frequency ($f \times \frac{2}{h}$) |
|---|---|---|---|
| 1 - 4 | 6 | 3 | $6 \times \frac{2}{3} = 4$ |
| 4 - 6 | 30 | 2 | $30 \times \frac{2}{2} = 30$ |
| 6 - 8 | 44 | 2 | $44 \times \frac{2}{2} = 44$ |
| 8 - 12 | 16 | 4 | $16 \times \frac{2}{4} = 8$ |
| 12 - 20 | 4 | 8 | $4 \times \frac{2}{8} = 1$ |
Step 3: Visualization (Histogram)
Final Solution: The histogram represents the data distribution where the height of each rectangle is proportional to the frequency, adjusted for class width variations to maintain graphical accuracy.
More Questions from Class 9 Mathematics Statistics EXERCISE 12.1
- Q1(i): A survey conducted by an organisation for the cause of illness and death among the women between the ages $15 - 44$ (in years) worldwide, found the following figures (in %) (i) Represent the information given above graphically.
- Q1(ii): A survey conducted by an organisation for the cause of illness and death among the women between the ages $15 - 44$ (in years) worldwide, found the following figures (in %): (ii) Which condition is the major cause of women’s ill health and death worldwide?
- Q1(iii): A survey conducted by an organisation for the cause of illness and death among the women between the ages $15 - 44$ (in years) worldwide, found the following figures (in %): (iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.
- Q2(i): The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below. (i) Represent the information above by a bar graph.
- Q2(ii): The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below. (ii) In the classroom discuss what conclusions can be arrived at from the graph.
- Q3(i): Given below are the seats won by different political parties in the polling outcome of a state assembly elections: (i) Draw a bar graph to represent the polling results.
- Q3(ii): Given below are the seats won by different political parties in the polling outcome of a state assembly elections: (ii) Which political party won the maximum number of seats?
- Q4(i): The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table: (i) Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
- Q4(ii): The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table: (ii) Is there any other suitable graphical representation for the same data?
- Q4(iii): The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table: (iii) Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?
- Q5(i): The following table gives the life times of 400 neon lamps: (i) Represent the given information with the help of a histogram.
- Q5(ii): The following table gives the life times of 400 neon lamps: (ii) How many lamps have a life time of more than 700 hours?
- Q6: The following table gives the distribution of students of two sections according to the marks obtained by them: Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.
- Q7: The runs scored by two teams A and B on the first 60 balls in a cricket match are given below: Represent the data of both the teams on the same graph by frequency polygons. [Hint : First make the class intervals continuous.]
- Q8: A random survey of the number of children of various age groups playing in a park was found as follows: Draw a histogram to represent the data above.
- Q9(ii): 100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows: (ii) Write the class interval in which the maximum number of surnames lie.
CBSE Solutions for Class 9 Mathematics Statistics
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