# Frank Solutions for Chapter 23 Graphical Representation of Statistical Data Class 9 Mathematics ICSE

**Exercise 23.1**

**1. Harmeet earns Rs 50,000 per month. He budget for his salary as per the following table:**

**Draw a bar graph for the above data.**

**Answer**

The bar graph for the above data is as follows:

**2.** **The birth rate per thousand of the following states over a certain period is given below:**

**Draw a bar graph for the above data.**

**Answer**

The bar graph for the above data is shown below

**3. ****Fadil, a class IX student, scored marks in different subjects (each out of total 100) during his annual examination as given below**

**Draw horizontal bar graph for the above data.**

**Answer**

The horizontal bar graph for the above data is as follows:

**4.** **The number of students in different sections of class IX of a certain school is given in the following table.**

**Draw horizontal bar graph for the above data.**

**Answer**

The horizontal bar graph for the above data is given below

**5.**

**The number of students (boys and girls) of class IX participating in different activities during their annual day function is given below:**

**Draw a double bar graph for the above data.**

**Answer**

The double bar graph for the above data is shown below

**6.** **Draw a histogram for the following frequency distribution:**

**Answer**

This is an exclusive frequency distribution. We represent the class limits on the x-axis on a suitable scale and the frequencies on the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, we construct rectangles to obtain a histogram of the given frequency distribution.

The histogram for the above frequency distribution is shown below

**7. ****Draw a histogram for the following frequency table:**

**Answer**

We see that the class intervals are in an inclusive manner. First, we need to convert them into exclusive manner.

We take the true class limits on the x-axis on a suitable scale and the frequencies on the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, we construct rectangles to obtain a histogram of the given frequency distribution.

Here, as the class limits do not start from 0, we put a kink between 0 and the true lower boundary of the first class.

The histogram for the given frequency table is shown below

**8. ****Draw a histogram for the following cumulative frequency table:**

**Answer**

The histogram for the cumulative frequency table is shown below

**9. ****Draw a histogram for the following cumulative frequency table:**

**Answer:**

First convert the cumulative frequency table to an exclusive frequency distribution table.

**10. ****Draw a histogram and a frequency polygon for the following data:**

**Answer**

We represent the class limits on the x-axis and the frequencies on the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, we construct rectangles to obtain a histogram of the given frequency distribution.

Now,

Take the mid-points of the upper horizontal side of each rectangle. Join the mid-points of two imaginary class intervals, one on either side of the histogram, by line segments one after the other.

The histogram and a frequency polygon for a given data is as follows:

**11. ****Draw a histogram and a frequency polygon for the following data:**

**Answer**

We represent the class limits on the x-axis and the frequencies on the y-axis on a suitable scale. Taking class intervals as bases and the corresponding frequencies as heights, we construct rectangles to obtain a histogram of the given frequency distribution.

Now,

Take the mid-points of the upper horizontal side of each rectangle. Join the mid-points of two imaginary class intervals, one on either side of the histogram, by line segments one after the other.

Here, as the class limits do not start from 0, we put a kink between 0 and the lower

boundary of the first class.

The histogram and a frequency polygon of the given data is as follows

**12. ****Draw a frequency polygon for the following data:**

**Answer**

We take the class limits on the x-axis and the frequencies on the y-axis on suitable scales.

Now,

Find the class marks of all the class intervals. Locate the points (x_{1}, y_{1}) on the graph, where x_{1} denotes the class mark and y_{1} denotes the corresponding frequency. Join all the points plotted above with straight line segments. Join the first point and the last point to the points representing class marks of the class intervals before the first class interval and after the last class interval of the given frequency distribution.

Here, as the class limits do not start from 0, we put a kink between 0 and the lower boundary of the first class.

Frequency polygon for the given data is shown below

**13.** **Draw a frequency polygon for the following data:**

**Answer**

We take the class limits on the x-axis and the frequencies on the y-axis on suitable scales.

Now,

Find the class marks of all the class intervals. Locate the points (x_{1}, y_{1}) on the graph, where x_{1} denotes the class mark and y_{1} denotes the corresponding frequency. Join all the points plotted above with straight line segments. Join the first point and the last point to the points representing class marks of the class intervals before the first class interval and after the last class interval of the given frequency distribution

Here, as the class limits do not start from 0, we put a kink between 0 and the lower boundary of the first class

Frequency polygon for the given data is shown below

**14. ****Draw a frequency polygon for the following data:**

**Answer**

We see that the class intervals are in an inclusive manner. We first need to convert them into exclusive manner.

Now,

Find the class marks of all the class intervals. Locate the points (x_{1}, y_{1}) on the graph, where x_{1} denotes the class mark and y_{1} denotes the corresponding frequency. Join all the points plotted above with straight line segments. Join the first point and the last point to the points representing class marks of the class intervals before the first class interval and after the last class interval of the given frequency distribution.

Here, as the class limits do not start from 0, we put a kink between 0 and the lower boundary of the first class.

**15. ****Read the following bar graph and answer the following questions:**

**(a) What information is given by the graph?**

**(b) Which state is the largest producer of wheat?**

**(c) Which state is the largest producer of sugar?**

**(d) Which state has total production of wheat and sugar as its maximum?**

**(e) Which state has the total production of wheat and sugar minimum?**

**Answer**

(a) The given graph gives information about production of wheat and sugar in five different states (U.P, Bihar, W.B, M.P, Punjab)

(b) The largest producer of wheat is Punjab

(c) The largest producer of sugar is U.P.

(d) The state which has total production of wheat and sugar as its maximum is U.P.

(e) The state which has total production of wheat and sugar minimum is W.B.