Histograms

Q.

Question 6
The marks obtained (out of 100) by a class of 80 students are given below:

$\begin{array}{cc}\text{Marks}& \text{Number of students}\\ 10-20& 6\\ 20-30& 17\\ 30-50& 15\\ 50-70& 16\\ 70-100& 26\end{array}$

Construct a histogram to represent the data above.

Q.

Draw a histogram for the marks of students given below:

$\begin{array}{cccccc}Marks:& 0-10& 10-30& 30-45& 45-50& 50-60\\ No.ofstudents& 8& 32& 18& 10& 6\end{array}$

1. 

2. 

3. 

4. None of these

Q.

Question 4
Draw a histogram to represent the following grouped frequency distribution

$\begin{array}{cc}\text{Age(in years)}& \text{Number of teachers}\\ 20-24& 10\\ 25-29& 28\\ 30-34& 32\\ 35-39& 48\\ 40-44& 50\\ 45-49& 35\\ 50-54& 12\end{array}$

Q.

Question 4
Prepare a continuous grouped frequency distribution from the following data.

$\begin{array}{cc}\text{Mid-Point}& \text{Frequency}\\ 5& 4\\ 15& 8\\ 25& 13\\ 35& 12\\ 45& 6\end{array}$

Also, find the size of class intervals.

Q. The monthly profits (in Rs.) of 100 shops are distributed as follows:

Profits per shop:	0−50	50−100	100−150	150−200	200−250	250−300
No. of shops:	12	18	27	20	17	6

Draw the frequency polygon for it.

Q.

Question 3
Draw a histogram of the following distribution.

$\begin{array}{cc}\text{Height(in cm)}& \text{Number of students}\\ 150-153& 7\\ 153-156& 8\\ 156-159& 14\\ 159-162& 10\\ 162-165& 6\\ 165-168& 5\\ \text{Total}& 145\end{array}$

Q.

Draw, in the same diagram , a histogram and a frequency polygon to represent the following data which shows the monthly cost of living index of a city in a period of 2 years:

$\begin{array}{ccccccccc}\text{Cost of living index}& 440-460& 460-480& 480-500& 500-520& 520-540& 540-560& 560-580& 580-600\\ \text{No. of months}& 2& 4& 3& 5& 3& 2& 1& 4\end{array}$

Q. The following table gives the height of trees:

Height	No. of trees
Less than 7 Less than 14 Less than 21 Less than 28 Less than 35 Less than 42 Less than 49 Less than 56	26 57 92 134 216 287 341 360

Draw less than ogive and more than ogive.

Q.

$\begin{array}{cccccccc}\text{Class mark}& 12.5& 17.5& 22.5& 27.5& 32.5& 37.5& 42.5\\ \text{Frequency}& 12& 17& 22& 27& 30& 21& 16\end{array}$

(a) From the distribution, given above, construct a frequency table.

(b) Use the table obtained in part (a) to draw : (i) a histogram, (ii) an ogive.

Q. Question 3
The following table gives production yield per hectare of wheat of 100 farms of a village.
$$\begin{array}{ccccccc}Productionyield\left(inkg/ha\right)& 50-55& 55-60& 60-65& 65-70& 70-75& 75-80\\ Numberoffarms& 2& 8& 12& 24& 38& 16\end{array}$$
Change the distribution to a more than type distribution and draw its ogive.

Q. Draw an ogive to represent the following frequency distribution:

Class-interval:	0−4	5−9	10−14	15−19	20−24
Frequency:	2	6	10	5	3

Q.

What is histogram?

Q. The marks scored by 750 students in an examination are given in the form of a frequency distribution table:

Marks	No. of student	Marks	No. of students
600−640 640−680 680−720 720−760	16 45 156 284	760−800 800−840 840−880	172 59 18

Prepare a cumulative frequency table by less than method and draw an ogive.

Q.

The following table presents the number of illiterate males in the age group $(10–34)$ in a town

$\begin{array}{cccccc}\text{Age Group}& 10-14& 15-19& 20-24& 25-29& 30-34\\ \text{Number of males}& 300& 980& 800& 580& 290\end{array}$

Draw a histogram to represent the above data

1. 

2. 

3. None of these

4. 

Q.

From the given histogram find the cumulative frequency for class interval 20-30.

1. Bar Graph
2. Frequency Polygon
3. Pie Chart
4. Histogram

Q.

Question 10
To draw a histogram to represent the frequency distribution.
$\begin{array}{cccccc}\text{Class interval}& 5-10& 10-15& 15-25& 25-45& 45-75\\ \text{Frequency}& 6& 12& 10& 8& 15\end{array}$
The adjusted frequency for the class 25 - 45 is:

A) 6
B) 5
C) 3
D) 2

Q.

While drawing a histogram for the discontinuous grouped data, if in case, the class intervals are given in the inclusive form, then in order to convert them into exclusive form, we must,

1. subtract the adjustment factor from all the lower limits and add it to all upper limits.

2. subtract the adjustment factor from all the lower limits and from all upper limits.

3. add the adjustment factor to all the lower limits to all upper limits.

4. add the adjustment factor to all the lower limits and subtract it from all upper limits.

Q. Draw a more than ogive for the data given below which gives the marks of 100 students.

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of students	4	6	10	10	25	22	18	5

Q.

Look at the given Table and identify the correct Histogram which can be made using the data.

$\begin{array}{cc}\text{Marks}& \text{No.of students}\\ 0-10& 2\\ 10-20& 5\\ 20-30& 9\\ 30-40& 4\\ 40-50& 6\end{array}$

Take SCALE as : X-axis - 1cm = 10 Marks and Y-axis - 1cm = 2 students

1. 

2. 

3. 

4. 

Q. Find the median of the following frequency distribution:

Class	0-10	10-20	20-30	30-40	40-50
Frequency	2	12	22	8	6

Q.

If the cumulative frequency at a particular class interval 30 -35 is 19 and the cumulative frequency at the next class -interval i.e 35-40 is 27 , the frequency at 35-40 is __________

1. 10

2. 3

3. 18

4. 8

Q.

Which of the following shows the correct histogram for the given data:
$\begin{array}{ccccccc}\text{Class interval}& 20-25& 25-30& 30-35& 35-40& 40-45& 45-50\\ \text{Frequency}& 30& 24& 52& 28& 46& 100\end{array}$

1. 

2. 

3. 

4. 

Q.

Question 5 (i)
The following table gives the life times of neon lamps:
$\begin{array}{cc}\text{Length (in hours)}& \text{Number of lamps}\\ 300-400& 14\\ 400-500& 56\\ 500-600& 60\\ 600-700& 86\\ 700-800& 74\\ 800-900& 62\\ 900-1000& 48\end{array}$
(i) Represent the given information with the help of a histogram.

Q.

Find the number of nodes, arcs and regions in the following networks.

(i)

(ii)

(iii)

(iv)

Q.

Using the information from the given histogram which of the following is one of the points used to construct the corresponding ogive?

1. (28, 76)

2. (16, 20)

3. (9, 12)

4. (32, 81)

Q. The time required for students to do a science experiment and the number of students is shown in the following grouped frequency distribution table. Show the information by a histogram and also by a frequency polygon.

Time required for experiment (minutes)	20 - 22	22 - 24	24 - 26	26 - 28	28 - 30	30 - 32
No. of students	8	16	22	18	14	12

Q.

If we draw a histogram for the class interval 15 - 30, what will be the height of the bar?

1. 3
2. 7
3. 11
4. 4

Q.

The following table shows the class mark and frequency. Find the highest class interval that the data can have

$\begin{array}{cc}\text{Class Mark}& \text{Frequency}\\ 55& 8\\ 65& 6\\ 75& 18\\ 85& 25\\ 95& 12\end{array}$

1. 50-60

2. 90-100

3. 55-65

4. 100-105

Q. The height of 50 girls of class X of a school are recorded as follows:

Height (in cm)	135−140	140−145	145−150	150−155	155−160	160−165
Number of girls	5	8	9	12	14	2

Draw a more than type ogive for the above data. [CBSE 2014]

Q. Convert the given class intervals in exclusive form.