Chapters
Balbharati Balbharati Class 10 Mathematics 1 Algebra
Chapter 6: Statistics
Chapter 6: Statistics solutions [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 
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 
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 
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 
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 
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]
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 
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 
The following table shows the classification of number of vehicles and their speeds on MumbaiPune 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 
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]
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 
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 
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 
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]
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 
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 
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 
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]
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 classmark 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 8090?
Electricity bill (Rs)  0  200  200  400  400  600  600  800  800  1000 
Families  240  300  450  350  160 
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]
Age group(Yrs)  20  25  25  30  30  35  35 40 
No. of persons  80  60  35  25 
Subject  English  Marathi  Science  Mathematics  Social science  Hindi 
Marks  50  70  80  90  60  50 
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 
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 
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 ?
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]
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° 
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 
Cumulative frequencies in a grouped frequency table are useful to find . . .
(A) Mean  (B) Median  (C) Mode  (D) All of these 
The formula to find mean from a grouped frequency table is
(A)
\[\frac{x_i + A}{g}\]

(B)
\[\left( x_i  A \right)\]

(C)
\[\frac{x_i  A}{g}\]

(D)
\[\frac{A  x_i}{g}\]

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 
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 46 are . . . .
(A) (4, 8)  (B) (3, 5)  (C) (5, 8)  (D) (8, 4) 
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 
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 
Chapter 6: Statistics
Balbharati Balbharati Class 10 Mathematics 1 Algebra
Textbook solutions for Class 10th Board Exam
Balbharati solutions for Class 10th Board Exam Algebra chapter 6  Statistics
Balbharati solutions for Class 10th Board Exam 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, stepbystep solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Balbharati Class 10 Mathematics 1 Algebra solutions in a manner that help students grasp basic concepts better and faster.
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Concepts covered in Class 10th Board Exam Algebra chapter 6 Statistics are 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, Mean of Grouped Data, Histograms, Tabulation of Data, Inclusive and Exclusive Type of Tables, Median of Grouped Data, Frequency Polygon, Reading of Pie Diagram.
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