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 Statistical Methods Calculators 1. Mean, Median, Mode, Quartiles, Delices, Percentiles, Variance, Standard deviation for 1. Ungrouped data 2. Grouped data 3. Mixed Type data 2. Missing frequency 1. Frequency for ungrouped data 2. Frequency for grouped data 3.Statistics Graph 1. Histogram 2. Frequency Polygon 3. Frequency Curve 4. Less than type cumulative frequency curve 5. More than type cumulative frequency curve 4. Statistics Wording Problem 5. Arithmetic Mean, Geometric Mean, Harmonic Mean 1. Find Arithmetic mean(AM), Geometric mean(GM), Harmonic mean(HM) 2. Find X from Arithmetic mean(AM), Geometric mean(GM), Harmonic mean(HM) 3. Find Mean or Median or Mode from other two's 6. Combined Mean and Combined Standard deviation 7. Mean deviation about mean, median, mode for 1. Ungrouped data 2. Grouped data 8. Standard deviation and coefficient of variation for 1. Ungrouped data 2. Grouped data 3. Mixed data 9. Correlation Coefficient for 1. Ungrouped data 2. Grouped data 10. Rank Correlation Coefficient 11. Regression and Regression lines 1. Regression lines for X & Y and Class-X & Y 2. Regression from Regression Lines 3. Regression lines from average, standard deviation, Correlation Coefficient(r) 4. Regression lines from sum x, sum y, sum x^2, sum y^2, sum xy, n 12. Regression lines for Grouped data 13. Curve Fitting - Method of Least Square 1. straight line (y=a+bx) 2. second degree parabola (y=a+bx+cx^2) 3. cubic quation (y=a+bx+cx^2+dx^3)
 1.1 Mean, Median, Mode, Quartiles, Delices, Percentiles, Standard deviation for ungrouped data Calculate Mean, Median, Mode from the follwing data 85,96,76,108,85,80,100,85,70,95 Mean bar x = (sum x_i)/n= (85 + 96 + 76 + 108 + 85 + 80 + 100 + 85 + 70 + 95)/10= 880/10= 88Median :Observations in the ascending order are :70, 76, 80, 85, 85, 85, 95, 96, 100, 108 Here, n = 10 is even.M = (text{Value of } (n/2)^(th) text{ observation} + text{Value of } (n/2 + 1)^(th) text{ observation})/2= (text{Value of } (10/2)^(th) text{ observation} + text{Value of } (10/2 + 1)^(th) text{ observation})/2= (text{Value of }5^(th) text{ observation} + text{Value of }6^(th) text{ observation})/2= (85 + 85)/2= 85Mode : In the given data, the observation 85 occurs maximum number of times (3):. Z = 85
1.2 Mean, Median, Mode, Quartiles, Delices, Percentiles, Standard deviation for grouped data

1. The information regarding the no of children per family is given in the following table. Find the mean, median, mode of the data
 No of children 0 1 2 3 4 5 No of families 3 20 15 8 3 1

2. The frequency distribution of the marks obtained by 100 tudents in a test of Mathematics carrying 50 marks is given below. Find the Mean, median, Mode of the data.

 Marks obtained 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 No of students 8 15 20 45 12

1.3 Mean, Median, Mode for mixed type data
1. Calculate the mean and standard deviation for the following distribution
 Class 1 2 5 6-10 10-20 20-30 30-50 50-70 70-100 f 3 4 10 23 20 20 15 3 2

 2.1 Missing frequency for ungrouped data 1. Find missing frequency from the follwing data 18,14,15,19,15,a,12,15,16 and Mean=16Here 18,14,15,19,15,a,12,15,16Here Mean bar x = 16 and n = 9sum x_i = 18 + 14 + 15 + 19 + 15 + a + 12 + 15 + 16= a + 124Mean bar x = (sum x_i)/n16 = (a + 124)/9144 = a + 124a = 144 - 124a = 20
2.2 Missing frequency for grouped Data
1. The mean of a frequency distribution of 40 persons is 16.5. Find the missing frequencies.
 Class 0 - 5 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 f 1 7 11 ? ? 4 2

2. Mean of the following distribution is 18.1. Find the missing frequency.
 Class 5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 35 f 11 20 35 20 a 6

3. Statistics Graph
1. Histogram
2. Frequency Polygon
3. Frequency Curve
4. Less than type cumulative frequency curve
5. More than type cumulative frequency curve

1. The frequency distribution of the marks obtained by 100 tudents in a test of Mathematics carrying 50 marks is given below.
Draw Histogram, Frequency Polygon, Frequency Curve, Less than type cumulative frequency curve and More than type cumulative frequency curve of the data.

 Marks obtained 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 No of students 8 15 20 45 12
 Histogram Frequency Polygon Frequency Curve Less than type cumulative frequency curve More than type cumulative frequency curve
 4. Statistics Wording Problem 1. The mean of 10 observations is 12.5 . While calculating the mean one observation was by mistake taken as -8 instead of +8. Find the correct mean.Here Mean X = 12.5 and n = 10Sigma(X) =  X  × n = 12.5 × 10 = 125:. the correct sum Sigma(X) = 125 - (Wrong Observation) + (Correct Observation) = 125 - ( -8 ) + ( 8 ) = 141.:. "correct mean" = "correct sum" / n = 141 / 10 = 14.1. 2. The mean of 10 observations is 35 . While calculating the mean two observations were by mistake taken as 35 instead of 25 and 30 instead of 45. Find the correct mean.Here Mean X = 35 and n = 10Sigma X = X × n = 35 × 10 = 350:. the correct sum Sigma X = 350 - 35 + 25 - 30 + 45 = 355.:. text{correct mean} = text{correct sum}/n = 355/10 = 35.5.

 5. Arithmetic Mean, Geometric Mean, Harmonic Mean 1. Find Arithmetic mean, Geometric mean, Harmonic mean for ungrouped data like 2, 3, 4, 5, 6 2. Find X where Arithmetic mean(AM)=3.5 for ungrouped data 2, 3, X, 5 3. Find Mode when Mean=3 and Median=4
6. Combined Mean and Standard deviation
Find Combined Mean and Standard deviation
1. Find the combined Standard Deviation from the following data.
 A B No of Observations 40 60 Average 10 15 S.D. 1 2

2. Find the combined Standard Deviation from the following data.
 A B No of Observations 100 150 Average 250 420 S.D. 10 6.4

3. Find the combined Standard Deviation from the following data.
 A B No of Observations 100 150 S X 25000 42000 Variance 100 40.96

 7.1 Mean deviation about mean, median, mode for ungrouped data Find Mean deviation about mean, median, mode of the following observations. 1. 85, 96, 76, 108, 85, 80, 100, 85, 70, 95 2. 3, 13, 11, 11, 5, 4, 2 3. 3, 23, 13, 11, 15, 3, 5, 4, 2 4. 69, 66, 67, 69, 64, 63, 65, 68, 72 5. 4, 14, 12, 16, 6, 3, 1, 2, 3 6. 73, 70, 71, 73, 68, 67, 69, 72, 76, 71 7. 10, 50, 30, 20, 10, 20, 70, 30
7.2 Mean deviation about mean, median, mode for grouped data
Find Mean Deviation(M.D.) About Mean, Median, Mode for grouped data

1.Calculate mean deviation from mean for the following distribution.(from mode )
 Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 No. of srudent 6 5 8 15 7 6 3

2. Calculate mean deviation from median for the following distribution.
 Class 1-3 3-5 5-7 7-9 9-11 11-13 13-15 15-17 Frequency 6 53 85 56 21 26 4 4

3. Calculate mean deviation from median for the following distribution.
 Class 3-4.9 5-6.9 7-8.9 9-10.9 11-12.9 13-14.9 15-16.9 Frequency 5 8 30 82 45 24 6

4. Calculate mean deviation from median for the following distribution.
 x 0 1 2 3 4 5 6 7 8 9 10 11 12 f 15 16 21 10 17 8 4 2 1 2 2 0 2

 8.1 Standard deviation and coefficient of variation for ungrouped data Find Standard deviation of the following observations. 1. 85, 96, 76, 108, 85, 80, 100, 85, 70, 95 2. 3, 13, 11, 11, 5, 4, 2 3. 3, 23, 13, 11, 15, 3, 5, 4, 2 4. 69, 66, 67, 69, 64, 63, 65, 68, 72 5. 4, 14, 12, 16, 6, 3, 1, 2, 3 6. 73, 70, 71, 73, 68, 67, 69, 72, 76, 71 7. 10, 50, 30, 20, 10, 20, 70, 30
8.2 Standard deviation and coefficient of variation for grouped data
Find Standard Deviation(S.D.) and Coefficient of Variation for Grouped Data

1. Calculate the mean and standard deviation for the following distribution
 X 6 7 8 9 10 11 12 f 3 6 9 13 8 5 4

2. Calculate the mean,.and standard deviation for the following distribution
 Class 4.5-12.5 12.5-20.5 20.5-28.5 28.5-36.5 36.5-44.5 44.5-52.5 52.5-60.5 60.5-68.5 68.5-76.5 f 4 24 21 18 5 3 5 8 2

3. Calculate the mean and standard deviation for the following distribution
 x 18 19 20 21 22 23 24 25 26 27 f 3 7 11 14 18 17 13 8 5 4

4. Calculate the mean and standard deviation for the following distribution
 Class 50-55 45-50 40-45 35-40 30-35 35-30 20-25 f 25 30 40 45 80 110 170

8.3 Standard deviation and coefficient of variation for mixed data
Find Standard Deviation(S.D.) and Coefficient of Variation for Mixed Data
1. Calculate the mean and standard deviation for the following distribution
 Class 1 2 5 6-10 10-20 20-30 30-50 50-70 70-100 f 3 4 10 23 20 20 15 3 2

9.1 Correlation Coefficient for ungrouped data
Find Correlation Coefficient for ungrouped Data

1. Psychological tests of intelligence and of engineering ability were applied to 10 students. Here is a record of ungrouped date showing intelligence ratio (I.R.) and engineering ratio (E.R.). Calculate the coefficient of correlation
 Student: A B C D E F G H I J IR 105 104 102 101 100 99 98 96 93 92 ER 101 103 100 98 95 96 104 92 97 94

2. Calculate correlation coefficient for following weights (In inches) fathers X and their sons Y
 X 65 66 67 67 68 69 70 72 Y 67 68 65 68 72 72 69 71

3. The following are the results of IT examination
 Age of candidates Candidate appeared Successful candidate 13-14 200 124 14-15 300 180 15-16 100 65 16-17 50 34 17-18 150 99 18-19 400 252 19-20 250 145 20-21 150 81 21-22 25 12 22-23 75 33
Calculate the coefficient of correlation between age and successful candidates in the examination?
9.2 Correlation Coefficient for grouped data
Find Correlation Coefficient for grouped data

1. Calculate the correlation coefficient.
 Class-Y Class-X
90-100 100-110 110-120 120-130
50-55 4 7 5 2
55-60 6 10 7 4
60-65 6 12 10 7
65-70 3 8 6 3

2. Calculate the correlation coefficient.
 Y Class-X
18 19 20 21
350-400 1 4 6 10
300-350 2 6 8 5
250-300 3 5 4 2
200-250 4 4 2 1

10. Rank correlation coefficient
Find Rank correlation coefficient

1. Ten participants in a contest are ranked by two judges as follows
 x 1 6 5 10 3 2 4 9 7 8 f 6 4 9 8 1 2 3 10 5 7
Calculate the rank correlation coefficient.

2. The values of the same 15 student in two subject A and B are given below the two numbers within the brackets denoting the ranks of the same student in A and B respectively.
(1,10), (2,7), (3,2), (4,6), (5,4), (6,8), (7,3), (8,1), (9,11),(10,15), (11,9), (12, 5), (13, 14), (14,12), (15, 13). Find the rank correlation coefficient.

3. The rank of the same 16 students in statistics and biology are as follows. Brackets represent the rank of the students in Statistics and Biology.
(1,1), (2,10), (3,3),(4,4), (5,5), (6,7), (7,2), (8,6), (9,8), (10,11), (11,15), (12, 9), (13, 14), (14,12), (15,16), (16, 13). Find the rank correlation coefficient.

4. Ten competitors in a musical test were ranked by the three judges A, B andC in the following order:
 judge A 1 6 5 10 3 2 4 9 7 8 judge B 3 5 8 4 7 10 2 1 6 9 judge C 6 4 9 8 1 2 3 10 5 7
Using rank correlation method. Discuss which pair of judges has the nearest approach to common liking in music.

5. Calculate the coefficient of rank correlation from the following data
 x 60 34 40 50 45 41 22 43 42 66 64 46 f 75 32 34 40 45 33 12 30 36 72 41 57

6. Obtain the rank correlation coefficient for the following data.
 X 68 64 75 50 64 80 75 40 55 64 Y 62 58 68 45 81 60 68 48 50 70

7. Obtain the rank correlation coefficient for the following data.
 X 48 33 40 9 16 16 65 24 16 57 Y 13 13 24 6 15 4 20 9 6 19
11. Regression and Regression lines
Find Regression and Regression lines

1. Find the equation of regression lines and estimate y for x = 1 and x for y =4.
 X 3 2 -1 6 4 -2 5 7 Y 5 13 12 -1 2 20 0 -3

2. Find the equation of regression lines and correlation coefficient from the follwoing data.
 X 28 41 40 38 35 33 46 32 36 33 Y 30 34 31 34 30 26 28 31 26 31

3. The following information is obtained form the results of examination
 Marks in Stats Marks in Maths Average 39.5 47.5 S.D. 10.8 16.8
The correlation coefficient between x and y is 0.42. Obtain two regression lines and estimate y for x = 50 and x for y = 30.

4. The follwoing information is obtained for two variables x and y. Find the regression equations of y on x.
 S XY = 3467 S X = 130 S X^2 = 2288 n = 10 S Y = 220 S Y^2 = 8822

5. The regression equation of two variables are
5y = 9x - 22
20x = 9y + 350
Find the means of x and y. Also find the value of r.

6. The regression equations of two variables are
x + 2y - 5 = 0
2x + 3y - 8 = 0
Variance of x = V(x) = 12.
Find x, y and V(y).

12. Regression lines for grouped data
Find Regression Lines for grouped Data

1. Calculate the correlation coefficient.
 Class-Y Class-X
90-100 100-110 110-120 120-130
50-55 4 7 5 2
55-60 6 10 7 4
60-65 6 12 10 7
65-70 3 8 6 3

2. Calculate the correlation coefficient.
 Class-Y Class-X
18 19 20 21
350-400 1 4 6 10
300-350 2 6 8 5
250-300 3 5 4 2
200-250 4 4 2 1
13. Curve Fitting - Method of Least Square
Curve Fitting - Method of Least Square

1. Fit a straight line y = a + bx using the following data
 x 5 4 3 2 1 y 1 2 3 4 5

2. Fit a straight line y = a + bx using the following data
 x 3 5 7 9 11 y 2.3 2.6 2.8 3.2 3.5