8th Maths : Chapter 6 : Statistics : Frequency Distribution Table, Graphical Representation of the Frequency Distribution for Ungrouped Data

**Exercise
6.1**

** **

**1. Fill in the blanks:**

(i) Data
has already been collected by some other person is _____________ data. **[Answer: Secondary]**

(ii) The
upper limit of the class interval (25-35) is _____________. **[Answer: 35]**

(iii) The
range of the data 200, 15, 20, 103, 3, 196, is _____________. **[Answer: 197]**

(iv) If a
class size is 10 and range is 80 then the number of classes are _________. **[Answer:** **8]**

(v) Pie chart
is a __________ graph. **[Answer: circular]**

** **

**2. Say True or False:**

(i) Inclusive
series is a continuous series. **[Answer: False]**

(ii) Comparison
of parts of a whole may be done by a pie chart. **[Answer:
True]**

(iii) Media
and business people use pie charts. **[Answer: True]**

(iv) A pie
diagram is a circle broken down into component sectors. **[Answer: True]**

**3. Represent the following data in ungrouped
frequency table which gives the number of children in 25 families.**

**1,3,0,2,5,2,3,4,1,0,5,4,3,1,3,2,5,2,1,1,2,6,2,1,4**

**Solution:**

The data given is raw data.

Ascending order : 0, 1, 2, 3, 4, 5, 6

∴ Tabulating in frequency distribution table we get

** **

**4. Form a continuous frequency distribution
table for the marks obtained by 30 students in a X std public examination.**

**328, 470, 405, 375, 298, 326, 276, 362,
410, 255, 391, 370, 455, 229, 300, 183, 283, 366, 400, 495, 215, 157, 374, 306,
280, 409, 321, 269, 398, 200.**

**Solution:**

Maximum mark obtained = 495

Minimum marks obtained = 157

Range = Maximum value − Minimum value

Range = 495 − 157

= 338

If we take the class size as 50 then the number of class
intervals possible

= **Range / Class size **

= 338 / 50 = 6.76

≃ 7

** **

**5. A paint company asked a group of students
about their favourite colours and made a pie chart of their findings. Use the information
to answer the following questions.**

**(i) What percentage of the students like
red colour?**

**(ii) How many students liked green colour?**

**(iii) What fraction of the students liked
blue?**

**(iv) How many students did not like red
colour?**

**(v) How many students liked pink or blue?**

**(vi) How many students were asked about
their favourite colours?**

**Solution:**

Total percentage of students = 100%

∴ 50 students = 100% − (30% + 20% + 25% + 15%)

= 100% − 90%

50 students = 10%

10% of total students = 50

∴ 10/100 (total students) = 50

Total students = [ 50 × 100 ] / 10 = 500.

Total students = 500.

**i) **20% of the students like red colour.

**ii)** 15% of the students liked green colour.

[ 15 / 100 ] × 500 = 75 students liked green colour.

**iii)** 25% students liked blue ⇒ 25/100 students liked blue.

=> 1/4 students liked blue.

**iv) **Percentage of students liked red colour = 20%

Percentage of students did not like red colour

= 100% − 20%

= 80%

∴ Number of students did
not like red colour

= 80% of 500

= [ 80 / 100 ] × 500 = 400

400 students did not like red colour.

**v)** Students liked pink or blue = students liked pink + students
liked blue.

= 30% of 500 + 25% of 500

= ( [30/100] × 500 ) + ( [25/100] × 500 )

= 150 + 125

= 275

**vi)** Total number of students = 500.

500 students were asked about their favourite colour.

** **

**6. A survey gives the following information
of food items preferred by people. Draw a Pie chart. **

**Solution:**

Total number of people = 160 + 90 + 80 + 50 + 30 + 40 = 450

Converting the number of people prefer various food items into
components part of 360°

Central angle of a component = [ **Value of the component /
Total value ]** × 360

Food items preferred by people.

** **

**7. Income from various sources for Government
of India from a rupee is given below. **Draw a pie chart.

**Solution:**

Income from various sources for Government of India in a rupee.

** **

**8. Monthly expenditure of Kumaran’s family
is given below. Draw a suitable Pie chart.**

**Also**

**1. Find the amount spent for education
if Kumaran spends ₹6000 for Rent.**

**2. What is the total salary of Kumaran?**

**3. How much did he spend more for food
than education?**

**Solution:**

Monthly expenditure of Kumaran's family.

1. Given Kumaran spends ₹
6000 for Rent.

∴ 15% of total expenditure
= 6000

15/100 (Total Expenditure) = 6000

Total Expenditure = [6000 × 100] / 15

Total Expenditure = ₹ 40,000

Amount spend for education = 20% of total expenditure.

= [20 / 100] × 40,000

= ₹ 8000

2. Total salary of Kumaran = ₹ 40,000

3. Amount spend for food = 50% of (40,000) = [50/100] × 40,000 =
₹ 20,000

Amount spend for the food than education

= 20,000 − 8,000 =

= ₹ 12,000

**Answer:**

**Exercise 6.1**

**1. (i) Secondary (ii)
35 (iii)197 (iv) 8 (v) Circular **

**2. (i) False (ii) True
(iii) True (iv) True **

**5. (i) 20% (ii) 75
(iii) 1/4 (iv) 400 (v) 275 (vi) 500**

**8. (i) ₹8000 (ii)
₹40000 (iii) ₹12000 **

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 6.1 (Frequency Distribution Table, Graphical Representation) | Questions with Answers, Solution | Statistics | Chapter 6 | 8th Maths

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