Practice Questions

What type of data is a histogram used to represent?

List three key features of a bar graph.

A bar graph shows the number of students in different clubs in a school: Music Club (40 students), Sports Club (60 students), Science Club (50 students), Art Club (30 students). Based on this information, answer the following: (i) Identify the club with the maximum number of students. (ii) Identify the club with the minimum number of students. (iii) What is the number of students in the Science Club?

Name the three types of graphical representations of data discussed in the chapter 'Statistics'.

The following bar graph shows the preferred breakfast items for 60 students in a hostel. Analyze the graph to determine how many more students prefer 'Paratha' over 'Idli'.

The number of hours for which students of a particular class watched television during holidays is given below. Apply this data to construct a bar graph.

Calculate the class mark for the class interval $127-135$.

Examine the following frequency distribution table for a continuous variable. What is the class size?

A survey records the brand of mobile phone used by 100 people. Is it possible to create a frequency polygon for this data? Justify your answer.

How is the class-mark of a class interval calculated? State the formula.

The profits (in Lakh Rupees) of a company for the last five years are 25, 40, 32, 55, and 48. Justify why a bar graph is a more suitable representation for this data than a histogram.

Define a bar graph.

A student represents the population of five different countries using a histogram. Critique this choice of graphical representation and justify whether it is appropriate.

A student was asked to represent the data from the table below using a histogram.

Critique the process if the student (a) did not make the class intervals continuous, and (b) did not adjust the heights of the bars for varying class widths. Then, recreate the correct frequency table with continuous classes and adjusted frequencies to construct a proper histogram.

In a bar graph, what do the heights of the bars depend on?

Explain the main differences between a bar graph and a histogram.

Describe the steps to draw a frequency polygon without first drawing a histogram.

For the class interval 45.5 - 50.5, identify the following: (i) The lower class limit (ii) The upper class limit (iii) The class-mark

Explain why a 'kink' or a 'break' is used on an axis in a graph like a histogram.

Describe the complete process of constructing a bar graph. Use the following data as an example to explain the steps: The number of different fruit trees in an orchard are: Mango (50), Apple (35), Orange (40), Guava (25).

Summarize the method for drawing a histogram for a frequency distribution with continuous classes of uniform width. List the key steps involved in the process.

Analyze the histogram for a mathematics test and determine the number of students who scored marks in the interval 60-80.

In a histogram, the areas of the rectangles are proportional to the frequencies. If the class widths are unequal, how must the length of the rectangles be modified? Analyze and state the formula.

Propose a modification to the following class intervals to make them suitable for constructing a histogram: 10-19, 20-29, 30-39. Justify your proposal.

Analyze the following data on the number of goals scored by a football team in 20 matches. Construct a frequency distribution table and then draw a bar graph.

Scores: 1, 3, 2, 5, 4, 2, 1, 3, 2, 0, 1, 1, 2, 3, 4, 5, 2, 0, 1, 3

The weekly wages (in ₹) of 30 workers in a factory are given below. Apply this data to construct a histogram.

The ages of 40 teachers in a school are recorded as follows. The class intervals are 21–25, 26–30, and so on. Apply the method to make the class intervals continuous and state the new class interval for 36–40 and the new class size.

A survey of 100 households was conducted to find the number of electronic devices they own. Calculate the class marks and then use the data to construct a frequency polygon without drawing a histogram.

The distribution of pocket money (in ₹) of students of two classes, IX A and IX B, is given below. Represent the data of both classes on the same graph using frequency polygons. Compare the performance of the two classes.

The lengths of 60 plant leaves were measured correct to the nearest millimetre, and the data is presented below. Apply this data to draw a histogram. (Hint: Make the class intervals continuous first).

A bar graph is created to show the number of cars sold by a company each month for a year. A student suggests that the width of the bar for December should be made wider than other months because sales were highest in December. Critique this suggestion.

The mid-points of the class intervals of a frequency distribution are 12, 18, 24, 30, 36. Formulate the corresponding class intervals, assuming the classes are continuous and of equal size. Justify your method.

Formulate a frequency distribution table with 5 classes for the following raw data on the heights (in cm) of 20 plants. Justify your choice of class size.

Data: 62, 75, 88, 65, 71, 92, 81, 68, 77, 84, 90, 73, 66, 85, 79, 80, 94, 70, 76, 82.

Two frequency polygons, representing the runs scored per over by Team A and Team B in a cricket match, are drawn on the same graph. For the first 10 overs, the polygon for Team A is consistently above the polygon for Team B. For the next 10 overs, the polygon for Team B is consistently above Team A. Evaluate the performance of the two teams and propose a conclusion.

Explain the concept of a frequency polygon. Describe the two methods for its construction.

Why is it necessary to adjust the lengths of rectangles in a histogram when the class intervals have varying widths?

Design a survey question and a corresponding data table structure to collect data on the monthly pocket money received by students in your class. The collected data should be suitable for representation by a histogram with at least three different class widths. Justify your design.

Evaluate whether a frequency polygon or a histogram is a better tool for comparing the distribution of marks for two different classes on the same axes. Justify your choice.

Design a complete statistical project to compare the consistency in batting performance of two cricket players, Player A and Player B, based on their scores in the last 15 matches. Your design must propose:

a) The most suitable graphical representation and justify its choice over other methods. b) A hypothetical data set for the 15 matches for both players. c) A step-by-step process to create the proposed graphical representation from the data.

Examine the following frequency polygon and answer the questions: (i) What is the class size? (ii) Which class has the maximum frequency? (iii) What is the frequency of the class whose class mark is 35?

A student collected data on the number of hours 50 people exercise per week. They created a histogram where the area of each rectangle is proportional to the frequency. If a class interval 4-6 hours has a frequency of 15 and is represented by a rectangle of height 7.5 units, formulate the height of the rectangle for the class interval 8-12 hours which has a frequency of 12.

The following table shows the number of students of a school participating in different sports. Examine the data and construct a histogram with varying widths.

The data below represents the marks obtained by 30 students in a science test. Create a frequency distribution table with class intervals of varying widths, using at least 4 different class sizes. Justify your grouping strategy. Then, create the table of adjusted heights required to draw a correct histogram.

Data: 8, 15, 21, 25, 32, 35, 38, 40, 41, 44, 48, 50, 52, 55, 59, 60, 61, 65, 68, 70, 72, 75, 78, 81, 85, 88, 90, 92, 95, 99.

A survey on the daily screen time of a group of people is presented in the following table. A student draws a histogram using the 'Number of people' as the heights of the rectangles. Critique this approach and create the correct calculations for the adjusted heights.

A random survey of the number of children of various age groups playing in a park was conducted. Draw a histogram to represent the data below and then analyze it to find the age group with the maximum number of children per year of age interval.