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

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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?

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

Answers:

1. Yes
2. No
3. No
4. Yes
5. Yes

Question 2.
Fill in the blanks

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

Answers:

1. frequency
2. proportional
3. Histogram
4. 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