# Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board chapter 6 - Statistics [Latest edition]

## Chapter 6: Statistics

Practice Set 6.1Practice Set 6.2Practice Set 6.3Practice Set 6.4Practice Set 6.5Practice Set 6.6Miscellaneous Problems 6
Practice Set 6.1 [Page 138]

### Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.1 [Page 138]

Practice Set 6.1 | Q 1 | Page 138

The following table shows the number of students and the time they utilized daily for their studies. Find the mean time spent by students for their studies by direct method.

 Time (hrs.) 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 No. of students 7 18 12 10 3
Practice Set 6.1 | Q 2 | Page 138

In the following table, the toll paid by drivers and the number of vehicles is shown. Find the mean of the toll by 'assumed mean' method.

 Toll (Rupees) 300 - 400 400 - 500 500 - 600 600 - 700 700 - 800 No. of vehicles 80 110 120 70 40
Practice Set 6.1 | Q 3 | Page 138

A milk centre sold milk to 50 customers. The table below gives the number of customers and the milk they purchased. Find the mean of the milk sold by direct method.

 Milk Sold (Litre) 1 - 2 2 - 3 3 - 4 4 - 5 5 - 6 No. of Customers 17 13 10 7 3
Practice Set 6.1 | Q 4 | Page 138

A frequency distribution table for the production of oranges of some farm owners is given below. Find the mean production of oranges by 'assumed mean' method.

 Production (Thousand rupees) 25 - 30 30 - 35 35 - 40 40 - 45 45 - 50 No. of Customers 20 25 15 10 10
Practice Set 6.1 | Q 5 | Page 138

A frequency distribution of funds collected by 120 workers in a company for the drought affected people are given in the following table. Find the mean of the funds by 'step deviation' method.

 Fund (Rupees) 0 - 500 500 - 1000 1000 - 1500 1500 - 2000 2000 - 2500 No. of workers 35 28 32 15 10
Practice Set 6.1 | Q 6 | Page 138

The following table gives the information of frequency distribution of weekly wages of 150 workers of a company. Find the mean of the weekly wages by 'step deviation' method.

 Weekly wages (Rupees) 1000 - 2000 2000 - 3000 3000 - 4000 4000 - 5000 No. of workers 25 45 50 30
Practice Set 6.2 [Pages 145 - 146]

### Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.2 [Pages 145 - 146]

Practice Set 6.2 | Q 1 | Page 145

The following table shows classification of number of workers and the number of hours they work in a software company. Find the median of the number of hours they work.

 Daily No. of hours 8 - 10 10 - 12 12 - 14 14 - 16 Number of workers 150 500 300 50
Practice Set 6.2 | Q 2 | Page 145

The frequency distribution table shows the number of mango trees in a grove and their yield of mangoes. Find the median of data.

 No. of Mangoes 50 - 100 100 - 150 150 - 200 200 - 250 250 - 300 No. of trees 33 30 90 80 17

Practice Set 6.2 | Q 3 | Page 145

The following table shows the classification of number of vehicles and their speeds on Mumbai-Pune express way. Find the median of the data.

 Average Speed of Vehicles(Km/hr) 60 - 64 64 - 69 70 - 74 75 - 79 79 - 84 84 - 89 No. of vehicles 10 34 55 85 10 6
Practice Set 6.2 | Q 4 | Page 146

The production of electric bulbs in different factories is shown in the following table. Find the median of the productions.

 No. of bulbs produced (Thousands) 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 No. of factories 12 35 20 15 8 7 8
Practice Set 6.3 [Page 149]

### Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.3 [Page 149]

Practice Set 6.3 | Q 1 | Page 149

The following table shows the information regarding the milk collected from farmers on a milk collection centre and the content of fat in the milk, measured by a lactometer. Find the mode of fat content.

 Content of fat (%) 2 - 3 3 - 4 4 - 5 5 - 6 6 - 7 Milk collected (Litre) 30 70 80 60 20
Practice Set 6.3 | Q 2 | Page 149

Electricity used by some families is shown in the following table. Find the mode for use of electricity.

 Use of electricity (Unit) 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 100 - 120 No. of families 13 50 70 100 80 17
Practice Set 6.3 | Q 3 | Page 149

Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk.

 Milk (Litre) 1 - 3 3 - 5 5 - 7 7 - 9 9 - 11 11 - 13 No. of hotels 7 5 15 20 35 18
Practice Set 6.3 | Q 4 | Page 149

Grouped frequency distribution of supply of milk to hotels and the number of hotels is given in the following table. Find the mode of the supply of milk.

 Age (years) Less than 5 5 - 9 10 - 14 15 - 19 20 - 24 25 - 29 No. of patients 38 32 50 36 24 20
Practice Set 6.4 [Page 153]

### Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.4 [Page 153]

Practice Set 6.4 | Q 1 | Page 153

Draw a histogram of the following data.

 Height of student (cm) 135 - 140 140 - 145 145 - 150 150 - 155 No. of students 4 12 16 8
Practice Set 6.4 | Q 2 | Page 153

The table below shows the yield of jowar per acre. Show the data by histogram.

 Yield per acre (quintal) 2 - 3 4 - 5 6 - 7 8 - 9 10 - 11 No. of farmers 30 50 55 40 20
Practice Set 6.4 | Q 3 | Page 153

In the following table, the investment made by 210 families is shown. Present it in the form of a histogram.

 Investment(Thousand Rupees) 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 No. of families 30 50 60 55 15
Practice Set 6.4 | Q 4 | Page 153

Time alloted for the preparation of an examination by some students is shown in the table. Draw a histogram to show the information.

 Time (minutes) 60 - 80 80 - 100 100 - 120 120 - 140 140 - 160 No. of students 14 20 24 22 16
Practice Set 6.5 [Page 157]

### Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.5 [Page 157]

Practice Set 6.5 | Q 1 | Page 157

Observe the following frequency polygon and write the answers of the questions below it.

(1) Which class has the maximum number of students ?
(2) Write the classes having zero frequency.
(3) What is the class-mark of the class, having frequency of 50 students ?
(4) Write the lower and upper class limits of the class whose class mark is 85.
(5) How many students are in the class 80-90?

Practice Set 6.5 | Q 2 | Page 157
Show the following data by a frequency polygon.
 Electricity bill (Rs) 0 - 200 200 - 400 400 - 600 600 - 800 800 - 1000 Families 240 300 450 350 160
Practice Set 6.5 | Q 3 | Page 157
The following table shows the classification of percentages of marks of students and the number of students. Draw a frequency polygon from the table.
 Result (Percentage) 30 - 40 40 - 50 50 - 60 60 -70 70 - 80 80 - 90 90 - 100 No. of students 7 33 45 65 47 18 5
Practice Set 6.6 [Pages 163 - 164]

### Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.6 [Pages 163 - 164]

Practice Set 6.6 | Q 1 | Page 163
The age group and number of persons, who donated blood in a blood donation camp is given below. Draw a pie diagram from it.
 Age group(Yrs) 20 - 25 25 - 30 30 - 35 35 -40 No. of persons 80 60 35 25
Practice Set 6.6 | Q 2 | Page 163
The marks obtained by a student in different subjects are shown. Draw a pie diagram showing the information.
 Subject English Marathi Science Mathematics Social science Hindi Marks 50 70 80 90 60 50
Practice Set 6.6 | Q 3 | Page 164

In a tree plantation programme, the number of trees planted by students of different classes is given in the following table. Draw a pie diagram showing the information.

 Standard 5 th 6th 7 th 8 th 9 th 10 th No. of trees 40 50 75 50 70 75
Practice Set 6.6 | Q 4 | Page 164

The following table shows the percentages of demands for different fruits registered with a fruit vendor. Show the information by a pie diagram.

 Fruits Mango Sweet lime Apples Cheeku Oranges Percentages of demand 30 15 25 20 10
Practice Set 6.6 | Q 5.1 | Page 164

The pie diagram in figure shows the proportions of different workers in a town. Answer the following question with its help.
If the total workers is 10,000; how many of them are in the field of construction ?

Practice Set 6.6 | Q 5.2 | Page 164

The pie diagram in figure shows the proportions of different workers in a town. Answer the following question with its help.

How many workers are working in the administration ?

Practice Set 6.6 | Q 5.3 | Page 164

The pie diagram in figure shows the proportions of different workers in a town. Answer the following question  with its help.

What is the percentage of workers in production ?

Practice Set 6.6 | Q 6 | Page 164

The annual investments of a family are shown in the adjacent pie diagram. Answer the following questions based on it.
(1) If the investment in shares is Rs 2000/, find the total investment.
(2) How much amount is deposited in bank ?
(3) How much more money is invested in immovable property than in mutual fund ?
(4) How much amount is invested in post ?

Miscellaneous Problems 6 [Pages 164 - 168]

### Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Miscellaneous Problems 6 [Pages 164 - 168]

Miscellaneous Problems 6 | Q 1.1 | Page 164

Find the correct answer from the alternatives given.
The persons of O– blood group are 40%. The classification of persons based on blood groups is to be shown by a pie diagram. What should be the measures of angle for the persons of O– blood group?

• 114°

• 140°

• 104°

• 144°

Miscellaneous Problems 6 | Q 1.2 | Page 164

Find the correct answer from the alternatives given.
Different expenditures incurred on the construction of a building were shown by a pie diagram. The expenditure Rs 45,000 on cement was shown by a sector of central angle of 75°. What was the total expenditure of the construction ?

• 2,16,000

• 3,60,000

• 4,50,000

• 7,50,000

Miscellaneous Problems 6 | Q 1.3 | Page 164

Find the correct answer from the alternatives given.

Cumulative frequencies in a grouped frequency table are useful to find . . .

• Mean

• Median

• Mode

• All of these

Miscellaneous Problems 6 | Q 1.4 | Page 164

Find the correct answer from the alternatives given.

The formula to find mean from a grouped frequency table is  $X = A + \frac{\sum f_i u_i}{\sum f_i} \times hg$ .

• $\frac{x_i + A}{g}$

• $\left( x_i - A \right)$

• $\frac{x_i - A}{g}$

• $\frac{A - x_i}{g}$
Miscellaneous Problems 6 | Q 1.5 | Page 164

Find the correct answer from the alternatives given.

 Distance Covered per litre (km) 12 - 14 14 - 16 16 - 18 18 - 20 No. of cars 11 12 20 7

The median of the distances covered per litre shown in the above data is in the group . . . . . .

• 12-14

• 14 - 16

• 16 - 18

• 18-20

Miscellaneous Problems 6 | Q 1.6 | Page 164

Find the correct answer from the alternatives given.

 No. of trees planted by each student 1 - 3 4 - 6 7 - 9 10 - 12 No. of students 7 8 6 4

The above data is to be shown by a frequency polygon. The coordinates of the points to show number of students in the class 4-6 are . . . .

• (4, 8)

• (3, 5)

• (5, 8)

• (8, 4)

Miscellaneous Problems 6 | Q 2 | Page 165

The following table shows the income of farmers in a grape season. Find the mean of their income.

 Income (Thousand Rupees) 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Farmers 10 11 15 16 18 14
Miscellaneous Problems 6 | Q 3 | Page 165

The loans sanctioned by a bank for construction of farm ponds are shown in the following table. Find the mean of the loans.

 Loan (Thousand Rupees) 40 - 50 50 - 60 60 - 70 70 - 80 80 - 90 No. of farm ponds 13 20 24 36 7
Miscellaneous Problems 6 | Q 4 | Page 166

The weekly wages of 120 workers in a factory are shown in the following frequency distribution table. Find the mean of the weekly wages.

 Weekly wages (Rupees) 0 - 2000 2000 - 4000 4000 - 6000 6000 - 8000 No. of workers 15 35 50 20
Miscellaneous Problems 6 | Q 5 | Page 166

The following frequency distribution table shows the amount of aid given to 50 flood affected families. Find the mean of the amount of aid.

 Amount of aid (Thosand rupees) 50 - 60 60 - 70 70 - 80 80 - 90 90 - 100 No. of families 7 13 20 6 4
Miscellaneous Problems 6 | Q 6 | Page 166

The distances covered by 250 public transport buses in a day is shown in the following frequency distribution table. Find the median of the distance.

 Distance (km) 200 - 210 210 - 220 220 - 230 230 - 240 240 - 250 No. of buses 40 60 80 50 20
Miscellaneous Problems 6 | Q 7 | Page 166

The prices of different articles and demand for them is shown in the following frequency distribution table. Find the median of the prices.

 Price (Rupees) 20 less than 20 - 40 40 - 60 60 - 80 80 - 100 No. of articles 140 100 80 60 20
Miscellaneous Problems 6 | Q 8 | Page 166

The following frequency table shows the demand for a sweet and the number of customers. Find the mode of demand of sweet.

 Weight of sweet (gram) 0 - 250 250 - 500 500 - 750 750 - 1000 1000 - 1250 No. of customers 10 60 25 20 15
Miscellaneous Problems 6 | Q 9 | Page 166

Draw a histogram for the following frequency distribution.

 Use of electricity (Unit) 50 - 70 70 - 90 90 - 110 110 - 130 130 - 150 150 - 170 No. of families 150 400 460 540 600 350
Miscellaneous Problems 6 | Q 10 | Page 167

In a handloom factory different workers take different periods of time to weave a saree. The number of workers and their required periods are given below. Present the information by a frequency polygon.

 No. of days 8 - 10 10 - 12 12 - 14 14 - 16 16 - 18 18 - 20 No. of workers 5 16 30 40 35 14
Miscellaneous Problems 6 | Q 11 | Page 167

The time required for students to do a science experiment and the number of students is shown in the following grouped frequency distribution table. Show the information by a histogram and also by a frequency polygon.

 Time required for experiment (minutes) 20 - 22 22 - 24 24 - 26 26 - 28 28 - 30 30 - 32 No. of students 8 16 22 18 14 12
Miscellaneous Problems 6 | Q 12 | Page 167

Draw a frequency polygon for the following grouped frequency distribution table.

 Age of the donor (Yrs.) 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 No. of blood doners 38 46 35 24 15 12
Miscellaneous Problems 6 | Q 13 | Page 167

The following table shows the average rainfall in 150 towns. Show the information by a frequency polygon.

 Average rainfall (cm) 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 No. of towns 14 12 36 48 40
Miscellaneous Problems 6 | Q 14 | Page 167

Observe the adjacent pie diagram. It shows the percentages of number of vehicles passing a signal in a town between 8 am and 10 am
(1) Find the central angle for each type of vehicle.
(2) If the number of two-wheelers is 1200, find the number of all vehicles.

Miscellaneous Problems 6 | Q 15 | Page 167

The following table shows causes of noise pollution. Show it by a pie diagram.

 Construction Traffic Aircraft take offs Industry Trains 10% 50% 9% 20% 11%
Miscellaneous Problems 6 | Q 16 | Page 168

A survey of students was made to know which game they like. The data obtained in the survey is presented in the adjacent pie diagram. If the total number of students are 1000,

(1) How many students like cricket ?
(2) How many students like football ?
(3) How many students prefer other games ?

Miscellaneous Problems 6 | Q 17 | Page 168

Medical check up of 180 women was conducted in a health centre in a village. 50 of them were short of haemoglobin, 10 suffered from cataract and 25 had respiratory disorders. The remaining women were healthy. Show the information by a pie diagram.

Miscellaneous Problems 6 | Q 18 | Page 168

On an environment day, students in a school planted 120 trees under plantation project. The information regarding the project is shown in the following table. Show it by a pie diagram.

 Tree name Karanj Behada Arjun Bakul Kadunimb No. of trees 20 28 24 22 26

## Chapter 6: Statistics

Practice Set 6.1Practice Set 6.2Practice Set 6.3Practice Set 6.4Practice Set 6.5Practice Set 6.6Miscellaneous Problems 6

## Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board chapter 6 - Statistics

Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board chapter 6 (Statistics) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board chapter 6 Statistics are Ogives (Cumulative Frequency Graphs), Applications of Ogives in Determination of Median, Relation Between Measures of Central Tendency, Introduction to Normal Distribution, Properties of Normal Distribution, Graphical Representation of Data as Histograms, Concept of Pie Graph (Or a Circle-graph), Mean of Grouped Data, Tabulation of Data, Inclusive and Exclusive Type of Tables, Median of Grouped Data, Frequency Polygon, Graphical Representation of Data as Histograms, Concept of Pie Graph (Or a Circle-graph), Mode of Grouped Data.

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