### CBSE Assignments class 09 Mathematics

Mathematics Assignments & Worksheets  For  Class IX Chapter-wise mathematics assignment for class 09. Important and useful extra questions strictly according to the CBSE syllabus and pattern with answer key CBSE Mathematics is a very good platform for the students and is contain the assignments for the students from 9 th  to 12 th  standard.  Here students can find very useful content which is very helpful to handle final examinations effectively.  For better understanding of the topic students should revise NCERT book with all examples and then start solving the chapter-wise assignments.  These assignments cover all the topics and are strictly according to the CBSE syllabus.  With the help of these assignments students can easily achieve the examination level and  can reach at the maximum height. Class 09 Mathematics    Assignment Case Study Based Questions Class IX

### 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 :   $\overline{x}=\frac{\sum f_{i}x_{i}}{\sum f_{i}}$

2. Assumed mean method :  $\overline{x}=a+\frac{\sum f_{i}d_{i}}{\sum f_{i}}$

3. Step-Deviation method :  $\overline{x}=a+h\frac{\sum f_{i}u_{i}}{\sum f_{i}}$

 Where, a Assumed mean di xi-a ui di/h or (xi-a)/h h height of C.I.

Class mark=  $\frac{Upper\: Limit+Lower\: Limit}{2}$

Range =  Highest value - Lowest value

Class size = Upper limit - Lower limit

## MODE of Data in Statistics

Mode:  =  $l+\frac{f_{1}-f_{0}}{2f_{1}-f_{0}-f_{2}}\times h$

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:  = $l+\left ( \frac{\frac{N}{2}-Cf}{f} \right )\times h$

Median Class:-  Class corresponding to the  $Cf\geq \frac{N}{2}$   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 StatisticsSolve 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

1. Creative questions. Keep it up