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8th Maths : Chapter 6 : Statistics : Graphical Representation of the Frequency Distribution for Grouped Data : Exercise 6.2 : Text Book Back Numerical problems, Exercises Questions with Answers, Solution

**Exercise
6.2**

** **

**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]**

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]**

**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?**

**Answer:** No.

** **

**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.

** **

**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.

** **

**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 – 1/2 (gap between adjacent class
interval)

= 125 – 1/2 (1) = 124.5

Upper boundary = Upper limit + 1/2 (gap between the adjacent
class interval)

= 135 + 1/2 = 135.5

∴ The new frequency table is

** **

** 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), F(55,35) G (65, 43.), H (75, 50) to obtain the frequency
polygon ZABCDEFGHI.

Where I imagined class between 80 and 90.

** **

**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

Number of possible intervals = **Range / Class size**

= 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**

**9. Data is a collection of ________ **

(A) numbers

(B) words

(C) measurements

(D) all the
three

**[Answer: (D) all the three]**

**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]**

**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]**

**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]**

**13. Inclusive series is a ________series.**

(A) continuous

(B) discontinuous

(C) both

(D) none
of these

**[Answer: (B) discontinuous]**

**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]**

**15. The graphical representation of ungrouped
data is ________**

(A) histogram

(B) frequency
polygon

(C)pie chart

(D) all the
three

**[Answer: (C) pie chart]**

**16. Histogram is a graph of a ________
frequency distribution.**

(A) continuous

(B) discontinuous

(C) discrete

(D) none
of these

**[Answer: (A) continuous]**

**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]**

**18. The graphical representation of grouped
data is ________**

(A) bar graph

(B) pictograph

(C) pie chart

(D) histogram

**[Answer: (D)** **histogram]**

**Answer:**

**Exercise 6.2**

**1. (i) Yes (ii) No
(iii) No (iv) Yes (v) Yes**

**2. (i) Proportional
(ii) Histogram(iii) Grouped**

**3. (i) 330 (ii) 150
(iii) No **

**9. (d) all the three **

**10. (c) Frequency **

**11. (a) range **

**12. (b) grouped**

**13. (b) discontinuous**

**14. (b) Exclusive**

**15. (c) pie chart **

**16. (a) continuous**

**17. (a) frequenc y polygon **

**18. (d) histogram**

Tags : Questions with Answers, Solution | Statistics | Chapter 6 | 8th Maths , 8th Maths : Chapter 6 : Statistics

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8th Maths : Chapter 6 : Statistics : Exercise 6.2 (Graphical Representation of the Frequency Distribution for Grouped Data) | Questions with Answers, Solution | Statistics | Chapter 6 | 8th Maths

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