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Chapter 6: Statistics
Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.1 [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 
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 
Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.2 [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 
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 
Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.3 [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 
Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.4 [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 
Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.5 [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 
Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Practice Set 6.6 [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 question with its help.
If the total workers is 10,000; how many of them are in the field of construction ?
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 ?
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 ?
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 ?
Balbharati solutions for Mathematics 1 Algebra 10th Standard SSC Maharashtra State Board Chapter 6 Statistics Miscellaneous Problems 6 [Pages 164  168]
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°
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
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
Find the correct answer from the alternatives given.
The formula to find mean from a grouped frequency table is \[X = A + \frac{\sum f_i u_i}{\sum f_i} \times hg\] .
\[\frac{x_i + A}{g}\]
\[\left( x_i  A \right)\]
\[\frac{x_i  A}{g}\]
 \[\frac{A  x_i}{g}\]
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 . . . . . .
1214
14  16
16  18
1820
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 46 are . . . .
(4, 8)
(3, 5)
(5, 8)
(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 
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 
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 
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 
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 
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 
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 
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 
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 
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 
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 
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 twowheelers is 1200, find the number of all vehicles.
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% 
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 ?
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.
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
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, stepbystep 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.
Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Balbharati textbook solutions can be a core help for selfstudy and acts as a perfect selfhelp guidance for students.
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 Circlegraph), 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 Circlegraph), Mode of Grouped Data.
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