Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 6 Statistics Ex 6.2 Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 6 Statistics Ex 6.2

Question 1.

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

(i) The number of mountain climbers in the age group 20 to 60 in TamilNadu.

Answer:

Yes

(ii) Production of cycles in different years.

Answer:

No

(iii) The number of students in each class of a school.

Answer:

No

(iv) The number votes polled from 7 am to 6 pm in an election.

Answer:

Yes

(v) The wickets fallen from 1 over to 50th over in a one day cricket match.

Answer:

Yes

Question 2.

Fill in the blanks:

(i) The total area of the histogram is _________ to the total frequency of the given data.

Answer:

proportional

(ii) A graph that displays data that changes continuously over the periods of time is _________ .

Answer:

Histogram

(iii) Histogram is a graphical representation of_________ data.

Answer:

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?

Answer:

330 people (110 + 220)

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

Answer:

150 of them (100 + 50)

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

Answer:

No

Question 4.

Draw a histogram for the following data.

Answer:

The given (tata 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.

Answer:

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 loo people is given below. Construct a histogram and the frequency polygon imposed on it.

Answer:

The given distribution is discontinuous.

Converting into continuous distribution we have

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

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

Upper boundary = Upper limit + \(\frac { 1 }{ 2 }\) (gap between the 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.

Answer:

Finding the midpoints of the class interval we get.

Ages | Mid point (x) | No. of patients |

0 – 10 | 5 | 5 |

10 – 20 | 15 | 13 |

20 – 30 | 25 | 25 |

30 – 40 | 35 | 14 |

40 – 50 | 45 | 30 |

50 – 60 | 55 | 35 |

60 – 70 | 65 | 43 |

70 – 80 | 75 | 50 |

The points tobe 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 (j) Make a frequency distribution table taking a class size of 10 marks (ii) Draw a histogram and a frequency polygon.

Answer:

Maximum marks obtained = 89

Minimum marks obtained = 08

Range = Maximum marks – Minimim marks

= 89 – 08

= 81

Taking the class size = 10, then

= \(\frac{81}{10}\) = 8.1 = 9

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 9.

Data is a collection of _________

(A) numbers

(B) words

(C) measurements

(D) all the three

Answer:

(D) all the three

Question 10.

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 11.

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 12.

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 13.

Inclusive series is a _________series.

(A) continuous

(B) discontinuous

(C) both

(D) none of these

Answer:

(B) discontinuous

Question 14.

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 15.

The graphical representation of ungrouped data is ________

(A) histogram

(B) frequency polygon

(C) pie chart

(D) all the three

Answer:

(C) pie chart

Question 16.

Histogram is a graph of a ________ frequency distribution.

(A) continuous

(B) discontinuous

(C) discrete

(D) none of these

Answer:

(A) continuous

Question 17.

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 18.

The graphical representation of grouped data is _________

(A) bar graph

(B) pictograph

(C) pie chart

(D) histogram

Answer:

(D) histogram