# ICSE Solutions for Selina Concise Chapter 23 Graphical Representation (Histograms and Ogives) Class 10 Maths

### Exercise 23

1. Draw histograms for the following frequency distributions:

(i)

 Class Interval 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 12 20 26 18 10 6

(ii)

 Class Interval 10-16 16-22 22-28 28-34 34-40 Frequency 15 23 30 20 16

(iii)

 Class Interval 30-39 40-49 50-59 60-69 70-79 Frequency 24 16 09 15 20

(iv)

 Class Marks 16 24 32 40 48 56 64 Frequency 8 12 15 18 25 19 10

Solution

(i)

 Class Interval Frequency 0-10 12 10-20 20 20-30 26 30-40 18 40-50 10 50-60 06

Steps of construction:

(a) Taking suitable scales, mark the class intervals on x-axis and the frequencies on y-axis.

(b) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(ii)

 Class Interval Frequency 10-16 15 16-22 23 22-28 30 28-34 20 34-40 16

Steps of construction:

(a) Taking suitable scales, mark the class intervals on x-axis and frequency on y-axis.

(b) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(iii)

 Class Interval(Inclusive form) Class Interval(Exclusive Form) Frequency 30-39 29.5-39.5 24 40-49 39.5-49.5 16 50-59 49.5-59.5 09 60-69 59.5-69.5 15 70-79 69.5-79.5 20

Steps of construction:

(a) Convert the data into exclusive form. [Here, adjustment factor = 0.5]

(b) Taking suitable scales, mark the class intervals on x-axis and the frequency on y-axis.

(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(iv) From the given data:

 Class Marks Class Intervals Frequency 16 12-20 08 24 20-28 12 32 28-36 15 40 36-44 18 48 44-52 25 56 52-60 19 64 60-68 10

Steps of construction:

(a) Convert the class marks into class intervals.

(b) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

2. Draw cumulative frequency curve (ogive) for each of the following distributions:

(i)

 Class   Interval 10-15 15-20 20-25 25-30 30-45 35-40 Frequency 10 15 17 12 10 08

(ii)

 Class Interval 10-19 20-29 30-39 40-49 50-59 Frequency 23 16 15 20 12

Solution

(i)

 Class Interval Frequency 10-15 10 15-20 15 20-25 17 25-30 12 30-35 10 35-40 08

Steps of construction:

(a) Taking suitable scales, mark the class intervals on x-axis and the frequencies on y-axis.

(b) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(c) Join the mid-points of the rectangle to obtain the ogive.

(ii)

 Class Interval(Inclusive) Class Interval(Exclusive) Frequency CumulativeFrequency 10-19 9.5-19.5 23 23 20-29 19.5-29.5 16 39 30-39 29.5-39.5 15 54 40-49 39.5-49.5 20 74 50-59 49.5-59.5 12 86 Total 86

Steps of construction:

(a) Convert the data into exclusive form. [Here, adjustment factor = 0.5]

(b) Taking suitable scales, mark the class intervals on x-axis and the frequencies on y-axis.

(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(d) Join the mid-points of the rectangle to obtain the ogive.

3. Draw an ogive for each of the following distributions:

(i)

 Marks Obtained less than 10 less than 20 less than30 less than 40 less than 50 No. of Students 8 25 38 50 67

(ii)

 Age in years (less than) 10 20 30 40 50 60 70 Cumulative Frequency 0 17 32 37 53 58 65

Solution

(i)

 Marks Obtained No. of students (c.f.) less than 10 8 less than 20 25 less than 30 38 less than 40 50 less than 50 67

Steps Of construction:

(a) Plot the points (10, 8), (20, 25), (30, 38), (40, 50) and (50, 67) on the graph.

(b) Join them with free hand to obtain an ogive.

(ii)

 Age in years  (less than) Cumulative Frequency 10 0 20 17 30 32 40 37 50 53 60 58 70 65

Steps Of construction:

(a) Plot the points (10, 0), (20, 17), (30, 32), (40, 37), (50, 53), (60, 58) and (70, 65) on the graph.

(b) Join them with free hand to obtain an ogive.

4. Construct a frequency distribution table for the number given below, using the class intervals 21-30, 31-40 … etc.

75, 67, 57, 50, 26, 33, 44, 58, 67, 75, 78, 43, 41, 31, 21, 32, 40, 62, 54, 69, 48, 47, 51, 38, 39, 43, 61, 63, 68, 53, 56, 49, 59, 37, 40, 68, 23, 28, 36, 47

Use the table obtained to draw:

(i) a histogram (ii) an ogive

Solution

(i)

(ii)

Plot the points (30,4), (40,13), (50,22), (60,29), (70,37) and (80,40) on the graph and join them with free hand to obtain an ogive.