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# Balbharati solutions for Class 10th Board Exam Algebra chapter 6 - Statistics

## Chapter 6: Statistics

#### Chapter 6: Statistics solutions [Page 138]

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
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
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
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
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 30
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

#### Chapter 6: Statistics solutions [Pages 145 - 146]

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

#### Chapter 6: Statistics solutions [Page 149]

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
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
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
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

#### Chapter 6: Statistics solutions [Page 153]

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
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
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
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

#### Chapter 6: Statistics solutions [Page 157]

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?

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
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

#### Chapter 6: Statistics solutions [Pages 163 - 164]

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
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
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
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
Q 5 | Page 164

The pie diagram in figure shows the proportions of different workers in a town. Answer the following questions with its help.
(1) If the total workers is 10,000; how many of them are in the field of construction ?
(2) How many workers are working in the administration ?
(3) What is the percentage of workers in production ?

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 ?

#### Chapter 6: Statistics solutions [Pages 164 - 165]

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 ?

 (A) 114°) (B) 140° (C) 104° (D) 144°
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 ?

 (A) 2,16,000 (B) 3,60,000 (C) 4,50,000 (D) 7,50,000
Q 1.3 | Page 164

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

 (A) Mean (B) Median (C) Mode (D) All of these
Q 1.4 | Page 164

The formula to find mean from a grouped frequency table is

$X = A + \frac{\sum f_i u_i}{\sum f_i} \times hg$
 (A)   $\frac{x_i + A}{g}$ (B)   $\left( x_i - A \right)$ (C)   $\frac{x_i - A}{g}$ (D)   $\frac{A - x_i}{g}$

Q 1.5 | Page 164
 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 . . . . . .

 (A) 12 - 14 (B) 14 - 16 (C) 16 - 18 (D) 18 - 20
Q 1.6 | Page 164
 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 . . . .

 (A) (4, 8) (B) (3, 5) (C) (5, 8) (D) (8, 4)
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
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

## Balbharati solutions for Class 10th Board Exam Algebra chapter 6 - Statistics

Balbharati solutions for Class 10th Board Exam Algebra 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 Textbook for SSC Class 10 Mathematics 1 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10th Board Exam Algebra chapter 6 Statistics are Reading of Pie Diagram, Frequency Polygon, Tabulation of Data, Inclusive and Exclusive Type of Tables, Median of Grouped Data, Mean of Grouped Data, Histograms, Pie Diagram, 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 Histograms.

Using Balbharati Class 10th Board Exam solutions Statistics exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Balbharati Solutions are important questions that can be asked in the final exam. Maximum students of Maharashtra State Board Class 10th Board Exam prefer Balbharati Textbook Solutions to score more in exam.

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