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

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.

* 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.

## 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

## 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

1. Creative questions. Keep it up