For the questions with numbers 92 and 93, given above, draw a :
(i) Histogram
(ii) Frequency polygon
(iii) Frequency polygon using histogram.

Question

For the questions with numbers 92 and 93, given above, draw a : (i) Histogram (ii) Frequency polygon (iii) Frequency polygon using histogram.

KnowledgeBoat · Accepted Answer

(i) The frequency table of question 92:

C.I.	Frequency
0-12	12
12-24	16
24-36	15
36-48	10
48-60	18

Steps to draw Histogram:

On x-axis, mark the class intervals.
On y-axis, mark frequencies.
Construct rectangles with class-intervals as bases and the corresponding frequencies as heights.

For the questions with numbers 92 and 93, given above, draw a (i) Histogram (ii) Frequency polygon (iii) Frequency polygon using histogram. Chapterwise Revision (Stage 2), Concise Mathematics Solutions ICSE Class 9.

The frequency table of question 93:

Class interval	Cumulative frequency	frequency
1-10	7	7
11-20	15	15 - 7 = 8
21-30	30	30 - 15 = 15
31-40	42	42 - 30 = 12
41-50	60	60 - 42 = 18
51-60	75	75 - 60 = 15

The class intervals are inclusive, so first convert the classes into the exclusive form.

On converting the class intervals to exclusive form, we get the following actual class limits:

Class interval	frequency
0.5-10.5	7
10.5-20.5	8
20.5-30.5	15
30.5-40.5	12
40.5-50.5	18
50.5-60.5	15

Steps to draw Histogram:

On x-axis, mark the class intervals.
On the y-axis, mark frequencies.
Construct rectangles with class-intervals as bases and the corresponding frequencies as heights.

(ii) The frequency table of question 92:

C.I.	Class-mark	Frequency
0-12	$\dfrac{1}{2}(0 + 12) = 6$	12
12-24	$\dfrac{1}{2}(12 + 24) = 18$	16
24-36	$\dfrac{1}{2}(24 + 36) = 30$	15
36-48	$\dfrac{1}{2}(36 + 48) = 42$	10
48-60	$\dfrac{1}{2}(48 + 60) = 54$	18

Steps to draw frequency polygon:

Find the class-mark (mid-value) of each given class-intervals.

Class-mark = mid-value = $\dfrac{\text{Upper limit + Lower limit}}{2}$

On a graph paper, mark class-mark along x-axis and frequencies along y-axis.
On a graph paper, mark points taking values of class-marks along x-axis and the values of their corresponding frequencies along y-axis.
Draw line segments joining the consecutive points marked in step (3) above.

The frequency table of question 93:

Class interval	Class mark	frequency
0-0.5	$\dfrac{1}{2}(0 + 0.5) = 0.25$	0
0.5-10.5	$\dfrac{1}{2}(0.5 + 10.5) = 5.5$	7
10.5-20.5	$\dfrac{1}{2}(10.5 + 20.5) = 15.5$	8
20.5-30.5	$\dfrac{1}{2}(20.5 + 30.5) = 25.5$	15
30.5-40.5	$\dfrac{1}{2}(30.5 + 40.5) = 35.5$	12
40.5-50.5	$\dfrac{1}{2}(40.5 + 50.5) = 45.5$	18
50.5-60.5	$\dfrac{1}{2}(50.5 + 60.5) = 55.5$	15

Steps to draw frequency polygon:

Find the class-mark (mid-value) of each given class-intervals.

Class-mark = mid-value = $\dfrac{\text{Upper limit + Lower limit}}{2}$

On a graph paper, mark class-mark along x-axis and frequencies along y-axis.
On a graph paper, mark points taking values of class-marks along x-axis and the values of their corresponding frequencies along y-axis.
Draw line segments joining the consecutive points marked in step (3) above.

(iii) The frequency table of question 92:

C.I.	Class-mark	Frequency
0-12	$\dfrac{1}{2}(0 + 12) = 6$	12
12-24	$\dfrac{1}{2}(12 + 24) = 18$	16
24-36	$\dfrac{1}{2}(24 + 36) = 30$	15
36-48	$\dfrac{1}{2}(36 + 48) = 42$	10
48-60	$\dfrac{1}{2}(48 + 60) = 54$	18

Steps to draw frequency polygon using histogram:

On x-axis, mark the class intervals.
On y-axis, mark frequencies.
Construct rectangles with class-intervals as bases and the corresponding frequencies as heights.
Mark the mid-points at the top of each rectangle of the histogram drawn.
Also, mark the mid-point of the immediately lower class-interval ( in the given example, the immediately lower class-interval is -12-0) and mid-point of the immediately higher class-interval (in the given example the immediate upper class-interval is 60-72).
Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon.

The frequency table of question 93:

Class interval	Class mark	frequency
0.5-10.5	$\dfrac{1}{2}(0.5 + 10.5) = 5.5$	7
10.5-20.5	$\dfrac{1}{2}(10.5 + 20.5) = 15.5$	8
20.5-30.5	$\dfrac{1}{2}(20.5 + 30.5) = 25.5$	15
30.5-40.5	$\dfrac{1}{2}(30.5 + 40.5) = 35.5$	12
40.5-50.5	$\dfrac{1}{2}(40.5 + 50.5) = 45.5$	18
50.5-60.5	$\dfrac{1}{2}(50.5 + 60.5) = 55.5$	15

Steps to draw frequency polygon using histogram:

On x-axis, mark the class intervals.
On y-axis, mark frequencies.
Construct rectangles with class-intervals as bases and the corresponding frequencies as heights.
Mark the mid-points at the top of each rectangle of the histogram drawn.
Also, mark the mid-point of the immediately lower class-interval ( in the given example, the immediately lower class-interval is 0-0.5) and mid-point of the immediately higher class-interval (in the given example the immediate upper class-interval is 60.5-70.5).
Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon.

50	59	27	78	54	72
58	57	31	65	42	60
22	37	40	and	28

Mathematics

For the questions with numbers 92 and 93, given above, draw a :
(i) Histogram
(ii) Frequency polygon
(iii) Frequency polygon using histogram.

Statistics

Answer

Related Questions

Construct a cumulative frequency distribution table from the following frequency table :
C.I. Frequency
0-12 12
12-24 16
24-36 15
36-48 10
48-60 18

Construct a frequency table from the following cumulative frequency table :
Class interval Cumulative frequency
1-10 7
11-20 15
21-30 30
31-40 42
41-50 60
51-60 75

Find the mean of the following numbers :
62, 58, 84, 71, 68, 70, 53, 63, 56 and 65.

Find median for the following data :
50 59 27 78 54 72
58 57 31 65 42 60
22 37 40 and 28

Mathematics

For the questions with numbers 92 and 93, given above, draw a :(i) Histogram(ii) Frequency polygon(iii) Frequency polygon using histogram.

Statistics

Answer

Related Questions

Construct a cumulative frequency distribution table from the following frequency table :C.I.Frequency0-121212-241624-361536-481048-6018

Construct a frequency table from the following cumulative frequency table :Class intervalCumulative frequency1-10711-201521-303031-404241-506051-6075

Find the mean of the following numbers :62, 58, 84, 71, 68, 70, 53, 63, 56 and 65.

Find median for the following data :505927785472585731654260223740and28

For the questions with numbers 92 and 93, given above, draw a :
(i) Histogram
(ii) Frequency polygon
(iii) Frequency polygon using histogram.

Construct a cumulative frequency distribution table from the following frequency table :
C.I. Frequency
0-12 12
12-24 16
24-36 15
36-48 10
48-60 18

Construct a frequency table from the following cumulative frequency table :
Class interval Cumulative frequency
1-10 7
11-20 15
21-30 30
31-40 42
41-50 60
51-60 75

Find the mean of the following numbers :
62, 58, 84, 71, 68, 70, 53, 63, 56 and 65.

Find median for the following data :
50 59 27 78 54 72
58 57 31 65 42 60
22 37 40 and 28