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## Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 3 Chapter 4 Statistics Ex 4.2

Question 1.

Which of the following data can be represented in a histogram?

- The number of mountain climbers in the age group 20 to 60.
- Production of cycles in different years.
- The number of students in each class of a school.
- The number votes polled from 7 am to 6 pm in an election.
- The wickets fallen from 1 over to 50th over in a one day cricket match.

Answers:

- Yes
- No
- No
- Yes
- Yes

Question 2.

Fill in the blanks

- The area of the rectangles are proportional to the _______ given.
- The total area of the histogram is _______ to the total frequency of the given data.
- _______ is a graphical representation of continuous frequency distribution with rectangles.
- Histogram is a graphical representation of _______ data.

Answers:

- frequency
- proportional
- Histogram
- grouped

Question 3.

In a village, there are 570 people who have cell phones. An NGO survey their cell phone usage. Based on this survey a histogram is drawn. Answer the following questions.

(i) How many people use the cell phone for less than 3 hours?

Solution:

330 people (110+ 220)

(ii) How many of them use the cell phone for more than 5 hours?

Solution:

150 of them (100 + 50)

(iii) Are people using cell phone for less than 1 hour?

Solution:

No.

(iv) Give your suggestions on the data.

Solution:

People should minimise the usage of cell phones.

Question 4.

Draw a histogram for the following data.

Solution:

The given data is continuous frequency distribution taking class intervals on X axis and No. of students on Y-axis, the histogram is given below.

Question 5.

Construct a histogram from the following distribution of total marks of 40 students in a class.

Solution:

The given distribution is continuous taking marks on X axis and No. of students on Y-axis the histogram is constructed.

Question 6.

The distribution of heights (in cm) of 100 people is given below. Construct a histogram and the frequency polygon imposed on it.

Solution:

The given distribution is discontinuous.

Converting into continuous distribution we have

Lower boundary = lower limit – \(\frac { 1 }{ 2 } \) (gap between the adjacent class interval)

= 125 – \(\frac { 1 }{ 2 } \) (1) = 124.5

Upper boundary = Upper limit + \(\frac { 1 }{ 2 } \) (gap between adjacent class interval)

= 135 + \(\frac { 1 }{ 2 } \) = 135.5

∴ The new frequency table is

+

Question 7.

In a study of dental problem, the following data were obtained.

Represent the above data by a frequency polygon.

Solution:

Finding the midpoints of the class interval we get.

The points to be plotted are A (5,5), B (15, 13), C (25, 25), D (35, 14), E (45, 30), G (65, 43.), H (75, 50) to obtain the frequency polygon ZABCDEFGHI.

Where I imagined class between 80 and 90.

Question 8.

The marks obtained by 50 students in Mathematics are given below (i) Make a frequency distribution table taking a class size of 10 marks (ii) Draw a histogram and a frequency polygon.

Solution:

Maximum marks obtained = 89

Minimum marks obtained = 08

Range = Maximum marks – Minimum marks = 89 – 08 = 81

Taking the class size = 10, then

Now we have the continuous frequency table.

We will draw the histogram taking class interval in x axis and frequency in y axis as follows.

Objective Type Questions

Question 1.

Data is a collection of _______

(a) numbers

(b) words

(c) measurements

(d) all the three

Answer:

(d) all the three

Question 2.

The number of times an observation occurs in the given data is called _______

(a) tally marks

(b) data

(c) frequency

(d) none of these

Answer:

(c) frequency

Question 3.

The difference between the largest value and the smallest value of the given data is _______

(a) range

(b) frequency

(c) variable

(d) none of these

Answer:

(a) range

Question 4.

The data that can take values between a certain range is called _______

(a) ungrouped

(b) grouped

(c) frequency

(d) none of these

Answer:

(b) grouped

Question 5.

Inclusive series is a _______ series

(a) continuous

(b) discontinuous

(c) both

(d) none of these

Answer:

(b) discontinuous

Question 6.

In a class interval the upper limit of one class is the lower limit of the other class. This is _______ series.

(a) Inclusive

(b) exclusive

(c) ungrouped

(d) none of these

Answer:

(b) exclusive

Question 7.

The graphical representation of un grouped data is _______

(a) histogram

(b) frequency polygon

(c) pie chart

(d) all the three

Question 8.

Histogram is a graph of a _______ frequency distribution.

(a) continuous

(b) discontinuous

(c) discrete

(d) none of these

Answer:

(a) continuous

Question 9.

A _______ is a line graph for the graphical representation of the continuous frequency distribution.

(a) frequency polygon

(b) histogram

(c) pie chart

(d) bar graph

Answer:

(a) frequency polygon

Question 10.

The graphical representation of grouped data is _______

(a) bar graph

(b) pictograph

(c) pie chart

(d) histogram

Answer:

(d) histogram