Histograms

Q.

The following table gives the lifetimes of 400 neon lamps:
$\begin{array}{cccccccc}\text{Lifetime (in hr)}& 300-400& 400-500& 500-600& 600-700& 700-800& 800-900& 900-1000\\ \text{Number of lamps}& 14& 56& 60& 86& 74& 62& 48\end{array}$
(i) Reperesent the given information with the help of a histogram.
(ii) How may lamps have a lifetime of more than 700 hours?

Q.

Draw a histogram and the frequency polygon from the following data:
$\begin{array}{ccccccc}\text{Class interval}& 20-25& 25-30& 30-35& 35-40& 40-45& 45-50\\ \text{Frequency}& 30& 24& 52& 28& 46& 100\end{array}$

Q.

Draw a histogram to represent the following data:
$\begin{array}{cccccc}\text{Class interval}& 10-14& 14-20& 20-32& 32-52& 52-80\\ \text{frequency}& 5& 6& 9& 25& 21\end{array}$

Q.

Draw a histogram for the following data:

$\begin{array}{cccccccc}\text{Marks}& 10-15& 15-20& 20-25& 25-30& 30-40& 40-60& 60-80\\ \text{Number of candidates}& 7& 9& 8& 5& 12& 12& 8\end{array}$

Q.

100 surnames were randomly picked up from a local telephone directory and frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

$\begin{array}{cccccc}\text{Number of letters}& 1-4& 4-6& 6-8& 8-12& 12-20\\ \text{Number of surnames}& 6& 30& 44& 16& 4\end{array}$
(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the maximum number of surnames lie.

Q.

Draw a histogram for the frequency distribution of the following data:
$\begin{array}{cccccccc}\text{Class interval}& 8-13& 13-18& 18-23& 23-28& 28-33& 33-38& 38-43\\ \text{Frequency}& 320& 780& 160& 540& 260& 100& 80\end{array}$

Q.

The following table shows the number of illiterate persons in the age group (10-58 years) in a town:
$\begin{array}{cccccccc}\text{Age group (in years)}& 10-16& 17-23& 24-30& 31-37& 38-44& 45-51& 52-58\\ \text{Number of}& 175& 325& 100& 150& 250& 400& 525\\ \text{illiterate persons}& & & & & & & \end{array}$
Draw a histogram to represent the above data.

Q.

In a histogram the area of each rectangle is proportional to

(a) the class mark of the corresponding class interval

(b) the class size of the corresponding class tnterval

(c) frequency of the corresponding class interval

(d) cumulative frequency of the corresponding class interval

Q.

Construct a histogram for the following frequency distribution:
$\begin{array}{ccccccc}\text{Class interval}& 5-12& 13-20& 21-28& 29-36& 37-44& 45-52\\ \text{Frequency}& 6& 15& 24& 18& 4& 9\end{array}$

Q.

The heights of 75 stucents in a school are given below:
$\begin{array}{ccccccc}\text{Height (in cm)}& 130-136& 136-142& 142-148& 148-154& 154-160& 160-166\\ \text{Number of students}& 9& 12& 18& 23& 10& 3\end{array}$
Draw a histogram to represent the above data.

Q. Question 7
Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way.

$\begin{array}{cc}Classinterval& Frequency\\ \left(km/h\right)& \\ 30-40& 3\\ 40-50& 6\\ 50-60& 25\\ 60-70& 65\\ 70-80& 50\\ 80-90& 28\\ 90-100& 14\end{array}$

Draw a histogram and frequency polygon representing the data above.

Q.

In a histogram the class interval or the groups are taken along

(a) Y-axis (b) X-axis

(c) both of X and Y axis (c) in between X and Y axis

Q.

In a histogram, each class rectangle is constructed with base as

(a) frequency (b) class-intervals

(c) range (d) size of the class

Q. Construct a histogram for the following data:

Monthly School fee (in Rs):	30-60	60-90	90-120	120-150	150-180	180-210	210-240
No of Schools	5	12	14	18	10	9	4

Q.

The following table gives the life times of neon lamps:

Length (in hours)	Number of lamps
300 − 400 400 − 500 500 − 600 600 − 700 700 − 800 800 − 900 900 − 1000	14 56 60 86 74 62 48

(i) Represent the given information with the help of a histogram.

(ii) How many lamps have a lifetime of more than 700 hours?

Q.

A histogram, is a pictorial representation of the grouped data in which class intervals and frequency are respectively taken along

(a) vertical axis and horizontal axis

(b) vertical axis only

(c) horizontal axis only

(d) horizontal axis and vertical axis

Q.

A random survey of the number of children of various age groups playing in park was found as follows:

Age (in years)	Number of children
1 − 2 2 − 3 3 − 5 5 − 7 7 − 10 10 − 15 15 − 17	5 3 6 12 9 10 4

Draw a histogram to represent the data above.

Q.

100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

Number of letters	Number of surnames
1 − 4 4 − 6 6 − 8 8 − 12 12 − 20	6 30 44 16 4

(i) Draw a histogram to depict the given information.

(ii) Write the class interval in which the maximum number of surname lie.

Q.

The time taken, in seconds, to solve a problem by each of 25 pupils is as follows:

16, 20, 26, 27, 28, 30, 33, 37, 38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53 , 58, 59, 60, 64, 52, 20

(a) Constuct a frequency distibution fof these data, using a class interval of 10 seconds.

(b) Draw a histogram to represent the frequency distribution .

Q.

Question 1
The frequency distribution
$\begin{array}{ccccc}\text{Marks}& 0-20& 20-40& 40-60& 60-100\\ \text{Number of}& 10& 15& 20& 25\\ \text{students}& & & & \end{array}$

has been represented graphically as follows:


Do you think this representation is correct? Why?

Q. In a histogram the class intervals or the group are taken along

(a) Y-axis

(b) X-axis

(c) both of X-axis and Y-axis

(d) in between X and Y axis

Q.

i) Percentage of people in the height range of 149.5 -159.5cm is equal to ______

ii) Percentage difference between height group 159.5 - 169.5cm and 169.5 - 179.5cm

1. 30 , 16.66 %

2. 20 , 6.66%

3. 20 , 16.66 %

4. 30 , 6.66 %

Q. The time taken, in seconds, to solve a problem by each of 25 pupils is as follows:
16, 20, 26, 27, 28, 30, 33, 37, 38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52, 20

(a) Construct a frequency distribution for these data, using a class interval of 10 seconds.
(b) Draw a histogram to represent the frequency distribution.

Q.

This list shows the age at which $43$ U.S. Presidents began their terms.

$$\begin{gathered} 57,61,50,54,54,54,56,54,61,54,48,49,42, \\ 51,61,57,68,65,50,51,60,52,57,51,52,47,56,62,69 \\ 58,49,56,55,55,43,64,57,64,46,55,51,55,46 \end{gathered}$$

Before you can make a frequency table, you need to decide how to set up the age intervals. What is the BEST way to group these ages into six intervals?

Q.

The histogram shows the birth weights of 100 newborn babies.
Babies who weigh less than 5 lb are considered to have a low birth weight.
Babies who weigh 10 lb or more are considered to have a high birth weight.
Scale:
On X axis - 1cm = 5 lb
On Y axis - 1cm = 5 units

What percent of the babies had neither a low or a high birth weight?

1. 83%
2. 91%
3. 85%
4. 97%

Q.

The following data tells about the number of runs scored by 20 players in a ranji match. Arrange the given in grouped frequency distribution .

$\begin{array}{cccccccccc}11& 15& 23& 25& 31& 33& 39& 42& 43& 49\\ 51& 56& 65& 75& 79& 89& 99& 98& 92& 91\end{array}$
[2 MARKS]

Q. When constructing a histogram with non-uniform (unequal) class widths, we must ensure that the areas of the rectangles are proportional to the ___________.

1. Class frequencies
2. Range
3. Class sizes
4. Class width

Q.

Draw a histogram from the given data of a class students.

$\begin{array}{cc}Weight\left(kg\right)& Numberofstudents\\ 35.5-40.5& 4\\ 40.5-45.5& 15\\ 45.5-50.5& 12\\ 50.5-55.5& 13\\ 55.5-60.5& 6\end{array}$
[4 MARKS]

Q.

Fifty-five percent of doctors at a hospital prescribe a particular medication. A simulation with $200$ random samples of $50$ doctors each is shown. Describe how the sample percentages vary.

Q. In a histogram the area of each rectangle is proportional to

(a) the class mark of the corresponding class interval

(b) the class size of the corresponding class interval

(c) frequency of the corresponding class interval

(d) cumulative frequency of the corresponding class interval