SELINA Solution Class 9 Chapter 18 Statistics Exercise 18B

Question 1

Construct a frequency polygon for the following distribution:

Class-intervals	0-4	4 - 8	8 - 12	12 - 16	16 - 20	20 - 24
Frequency	4	7	10	15	11	6

Sol:

The frequency polygon is shown in the following figure

Steps:

(i) Drawing a histogram for the given data.

(ii) Marking the mid-point at the top of each rectangle of the histogram drawn.

(iii) Also, marking mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.

(iv) Joining the consecutive mid-points marked by straight lines to obtain the required frequency polygon.

Question 2

Construct a combined histogram and frequency polygon for the following frequency distribution:

Class-Intervals	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60
Frequency	3	5	6	4	2

Sol:

Steps:

1. Draw a histogram for the given data.

2. Mark the mid-point at the top of each rectangle of the histogram drawn.

3. Also, mark the mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.

4. Join the consecutive mid-point marked by straight lines to obtain the required frequency polygon.

5. The require combined histogram and frequency polygon are shown in the following figure:

Question 3

Construct a frequency polygon for the following data:

Class-Intervals	10 - 14	15 - 19	20 - 24	25 - 29	30 - 34
Frequency	5	8	12	9	4

Sol:

The class intervals are inclusive. We will first convert them into the exclusive form.

Class-Interval	Frequency
9.5 - 14.5	5
14.5 - 19.5	8
19.5 - 24.5	12
24.5 - 29.5	9
29.5 - 34.5	4

Steps:

1. Draw a histogram for the given data.
2. Mark the mid-point at the top of each rectangle of the histogram drawn.
3. Also, mark the mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.
4. Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon. 

The required frequency polygon is as follows:

Question 4

The daily wages in a factory are distributed as follows:

Daily wages (in Rs.)	125 - 175	175 - 225	225 - 275	275 - 325	325 - 375
Number of workers	4	20	22	10	6

Draw a frequency polygon for this distribution.

Sol:

Steps:

1. Draw a histogram for the given data.
2. Mark the mid-point at the top of each rectangle of the histogram drawn.
3. Also, mark the mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.
4. Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon.

The required frequency polygon is as follows:

Question 5.1

Draw frequency polygons for each of the following frequency distribution: 

(a) using histogram

(b) without using histogram

C.I	10 - 30	30 - 50	50 - 70	70 - 90	90 - 110	110 - 130	130 - 150
ƒ	4	7	5	9	5	6	4

Sol:

using histogram

C.I	ƒ
10 - 30	4
30 - 50	7
50 - 70	5
70 - 90	9
90 - 110	5
110 - 130	6
130 - 150	4

Steps:

1. 1. Draw a histogram for the given data.
   2. Mark the mid-point at the top of each rectangle of the histogram drawn.
   3. Also, mark the mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.
   4. Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon. 

Without using Histogram:

Steps: 

1. Find the class-mark (mid-value) of each given class-interval.
   class mark = mid-value = ${\displaystyle \frac{\text{Upper limit + Lower limit}}{2}}$
2. On a graph paper, mark class-marks along X-axis and frequencies along Y-axis.

3. On this graph paper, mark points taking values of class-marks along the X-axis and the values of their corresponding frequencies along Y-axis.

4. Draw line segments joining the consecutive points marked in step (3) above.

   C.I.	Class-mark	f
   -10 - 10	0	0
   10 - 30	20	4
   30 - 50	40	7
   50 - 70	60	5
   70 - 90	80	9
   90 - 110	100	5
   110 - 130	120	6
   130 - 150	140	4
   150 - 170	160	0

5. 

Question 5.2

Draw frequency polygons for each of the following frequency distribution:
(a) using histogram
(b) without using histogram

C.I	5 -15	15 -25	25 -35	35 - 45	45-55	55-65
ƒ	8	16	18	14	8	2

Sol:

Using Histogram:

C.I.	f
5 - 15	8
15 - 25	16
25 - 35	18
35 - 45	14
45 - 55	8
55 - 65	2

Steps:

1. Draw a histogram for the given data.
2. Mark the mid-point at the top of each rectangle of the histogram drawn.
3. Also, mark the mid-point of the immediately lower class-interval and mid-point of the immediately higher class-interval.
4. Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon.

Without using Histogram:
Steps:

1. Find the class-mark (mid-value) of each given class-interval.
2.  
3. On a graph paper, mark class-marks along X-axis and frequencies along Y-axis.
4. On this graph paper, mark points taking values of class-marks along the X-axis and the values of their corresponding frequencies along the Y-axis.
5.  
6. Draw line segments joining the consecutive points marked in step (3) above.
   

   C.I.	Class-mark	f
   -5 - 5	0	0
   5 - 15	10	8
   15 - 25	20	16
   25 - 35	30	18
   35 - 45	40	14
   45 - 55	50	8
   55 - 65	60	2
   65 - 75	70	0