Dictionary Rank of a Word | Permutations & Combinations

 PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

Math Assignment Ch-14 Class X | Statistics

Mathematics Assignment 
Class X, Chapter 14
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. 

Assignment on Statistics
Solve the following questions

1. Find the mean of the following 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

 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

 

 3.  If mean = 6 then find p.   Ans:- 7                                                             

X

Y

2

3

4

2

6

3

10

1

P+5

2

 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


 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

  6. If mean =18 then find p.           Ans:- 1,-3

X

Y

13

8

15

2

17

3

19

4

20+p

5p

23

6

 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

 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

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

 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

  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

12. Find median.         Ans: 40

Class Interval

Frequency

0-10

5

10-30

15

30-60

30

60-80

8

80-90

2

  13. 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


14. Find median.       Ans:-29.42

Class Interval

Frequency

1-10

10

11-20

21

21-30

51

31-40

45

41-50

26

15. 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

 16. 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


17. 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

 18. Calculate Mean, mode, median.

Ans : Median=52 ,     Mean= 51.63    &   Mode = 53.33

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

 19. 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


20. 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

21. 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

                                 

22. 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

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

24.  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



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