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Mathematics Lab Manual Class XII | 14 Activities

    Mathematics Lab Manual Class XII 14 lab activities for class 12 with complete observation Tables strictly according to the CBSE syllabus also very useful & helpful for the students and teachers. General instructions All these activities are strictly according to the CBSE syllabus. Students need to complete atleast 12 activity from the list of 14 activities. Students can make their own selection.

Math Assignment Ch-14 Class X | Statistics

Mathematics Assignment


Extra questions of statistics class 10, chapter 14, Important and board based questions based on chapter 14 of class 10

Chapter: 14(Statistics)
Formulas used to solve the Assignment on statistics

Methods of finding mean in grouped data:-

1. Direct method :   

2. Assumed mean method :  

3. Step-Deviation method :       

Where,

 

a

Assumed mean

di

xi-a

ui

di/h or (xi-a)/h

h

height of C.I.

 Class mark=  

Range =  Highest value - Lowest value

Class size = Upper limit - Lower limit

MODE of Data in Statistics

Mode:  =  

Where l = lower limit of the modal class,

 h = size of the class interval 

 f1 = frequency of the modal class

f0 = frequency of the class preceding the modal class,

f2 = frequency of the class succeeding the modal class.

Median of Data in Statistics

Median:  = 

Median Class:-  Class corresponding to the     is called median class

Where l= lower limit of median class                           

N = Sum of all observations

f = frequency of the median class.       

Cf= cumulative frequency of class  preceding the median class

 h= height of  median class

Empirical Formula of Data in Statistics

Empirical Formula:  Relation between mean, mode , median;-

      Mode=3 Median - 2 Mean

Empirical formula does not provide the same result in different situations. So, students should use it only when asked otherwise avoid it.

NOTE :- For finding median, height of class interval need not to be equal or class interval may be irregular.

* If median class is the first class –interval then cumulative frequency (Cf) of the preceding class interval should be taken as zero.

* For finding Mean class interval need not to be continuous.

* For finding Mode and Median class interval should be continuous. 

* For making class interval continuous we should subtract 0.5 from the lower limits and add 0.5 to the upper limits of all class intervals. 

Assignment on Statistics
Solve the following questions

PROBLEMS BASED ON MEAN

QUESTION1. Find the mean of the following ungrouped data :- Ans:- 3.52

Absent Students

No. of days

0

1

1

4

2

10

3

50

4

34

5

15

6

4

7

2

Total

120

QUESTION 2. Find the mean by using all 3 methods separately:-     Ans:-25.86

Marks

No. of Students

0-10

20

10-20

24

20-30

40

30-40

36

40-50

20

Total

14 0

QUESTION 3.  For the following data if mean = 6 then find the value of  p.   Ans:- 7                                                            

X

Y

2

3

4

2

6

3

10

1

P+5

2

QUESTION 4. If mean =56, then find  f1 & f2 .   Ans:- f1 = 11 &  f2 = 12

Class Interval

Frequency

0-20

16

20-40

f1

40-60

 25

60-80

16

80-100

f2

100-120

10

Total

90

QUESTION 5. If mean=50 then find f1 & f2.       Ans:- f1 =28 &  f2 = 24

Class Interval

Frequency

0-20

17

20-40

f1

40-60

 32

60-80

f2

80-100

19

Total

120

QUESTION 6. For the follwing data If mean =18 then find p.           Ans:- 1, -3

X

Y

13

8

15

2

17

3

19

4

20+p

5p

23

6


QUESTION 7. Find the mean by using all 3 methods.     Ans:- 165.502

Class Interval

Frequency

110-120

2

120-130

5

130-140

11

140-150

21

150-160

26

160-170

34

170-180

36

180-190

28

190-200

16


QUESTION 8.Find mean.       Ans: 12.38

Do we use here step-deviation method ? Why or Why not   

Class Interval

Frequency

0-6

11

6-10

10

10-14

7

14-20

4

20-28

4

28-38

3

38-40

1

No, we cannot use step deviation method here because height of the class intervals are not equal. So we can solve this question either by Direct Method or by Assumed mean method


QUESTION 9. Find arithmetic mean by using suitable method.     Ans:-196.8   

Class Interval

Frequency

0-80

22

80-160

35

160-240

44

240-320

25

320-400

24

PROBLEMS BASED ON MODE 

QUESTION 10. For the given data find mean & mode.              

Ans : Mean=26 & Mode=22.85

Class Interval

Frequency

More than 0

60

More than 10

56

More than 20

40

More than 30

20

More than 40

10

More than 50

3

QUESTION 11. Find mode.                   Ans:-18

Class Interval

Frequency

0-5

3

5-10

7

10-15

15

15-20

30

20-25

20

25-30

10

30-35

5

QUESTION 12. Find mode.              Ans:-63.75

Height

No. of Plants

More than 30

34

More than40

30

More than 50

27

More than 60

19

More than 70

8

More than 80

2

QUESTION 13. If mode of the following frequency distribution is 55, then find the value of x.
Ans: x = 5

Class Interval

Frequency

0-15

10

15-30

7

30-45

x

45-60

15

60-75

10

75-90

12


QUESTION 14. Mode of the following data is 45, find x and y ,given n= 50
Ans x=10, y = 2

Class Interval

Frequency

10-20

4

20-30

8

30-40

x

40-50

12

50-60

10

60-70

4

70-80

y

PROBLEMS BASED ON MEDIAN

QUESTION 15. Find median.         Ans: 40

Class Interval

Frequency

0-10

5

10-30

15

30-60

30

60-80

8

80-90

2

QUESTION 16. Find median.       Ans:-29.42

Class Interval

Frequency

1-10

10

11-20

21

21-30

51

31-40

45

41-50

26

QUESTION 17. If median=46 then find x & y.        Ans: x = 33.5 & y = 45.5

Class Interval

Frequency

10-20

12

20-30

30

30-40

x

40-50

65

50-60

y

60-70

25

70-80

18

Total

229

QUESTION 18. If median =35 then find f1 & f2.       

Ans: f1=35 & f2= 25

Class Interval

Frequency

0-10

10

10-20

20

20-30

f1

30-40

40

40-50

f2

50-60

25

60-70

15

Total

170

QUESTION 19. Find median ages.      Ans:- 35.76

Ages

No. of men

Less than 20

2

Less than 25

6

Less than 30

24

Less than 35

45

Less than 40

78

Less than 45

89

Less than 50

92

Less than 55

98

Less than 60

100

QUESTION 20. 
Find the unknown entries a, b, c, d, e, f in the following distribution if total no. of students is 50

class interval

frequency

c.f.

150-155

12

a

155-160

b

25

160-165

10

c

165-170

d

43

170-175

e

48

175-180

2

f

MISCELLANEOUS PROBLEMS ON MEAN, MODE, MEDIAN 

QUESTION 21. 

If mode = 24.5 and mean is 29.75 then find median by using empirical formula.    [Ans: 28]

QUESTION 22.  
Find the mode and median of the data.   Ans[Mode= 9.56, Median= 12.19]

Class Interval

Frequency

5-8

40

8-11

90

11-14

44

14-17

58

17-20

53

20-23

10

QUESTION 23. Calculate Mean, mode, median.     Ans : Mean = 51.63, Mode = 53.33, Median = 52


Marks

No of Students

More than 0

80

More than 10

76

More than 20

71

More than 30

65

More than 40

57

More than 50

43

More than 60

28

More than 70

15

More than 80

10

More than 90

8

More than 100

0

HIGHER ORDER THINKING SKILLS (HOTS)

QUESTION 24. Find the missing frequency (f1, f2, and f3) in the following data, when it is given that f2 : f3 = 4 : 3 and mean = 50

Answer: f1 = 28, f2 = 32 and f3 = 24

Class Interval

Frequency

0-20

17

20-40

f1

40-60

f2

60-80

f3

80-100

19

Total

120

Solution Hint:  Use direct method to solve this question

For easy calculation use step deviation method and take assume mean (a) in front of f1


QUESTIONS DELETED FROM CBSE SYLLABUS

QUESTION 25. Find median by using less than ogive & actual calculation.                              

Ans:- 27.5

Marks

No. of Students

Less than 10

4

Less than 20

10

Less than 30

30

Less than 40

40

Less than 50

47

Less than 60

50


QUESTION 26. Draw less than ogive & more than type ogive and find median.    Ans:-34.33

Class Interval

Frequency

0-10

4

10-20

8

20-30

11

30-40

15

40-50

12

50-60

6

60-70

3

THANKS FOR YOUR VISIT
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