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1.1 Ungrouped data 85,96,76,108,85,80,100,85,70,95
1. Mean, Median and Mode for ungrouped data
2. Quartiles, Deciles and Percentiles for ungrouped data
3. Population Variance, Standard deviation and coefficient of variation for ungrouped data
4. Sample Variance, Standard deviation and coefficient of variation for ungrouped data
5. Population Skewness, Kurtosis for ungrouped data
6. Sample Skewness, Kurtosis for ungrouped data
7. Geometric mean, Harmonic mean for ungrouped data
8. Mean deviation, Quartile deviation, Decile deviation, Percentile deviation for ungrouped data
1.2 Grouped data
 Class 50-55 45-50 40-45 35-40 30-35 35-30 20-25 f 25 30 40 45 80 110 170
1. Mean, Median and Mode for grouped data
2. Quartiles, Deciles and Percentiles for grouped data
3. Population Variance, Standard deviation and coefficient of variation for grouped data
4. Sample Variance, Standard deviation and coefficient of variation for grouped data
5. Population Skewness, Kurtosis for grouped data
6. Sample Skewness, Kurtosis for grouped data
7. Geometric mean, Harmonic mean for grouped data
8. Mean deviation, Quartile deviation, Decile deviation, Percentile deviation for grouped data
1.3 Mixed data
 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
1. Mean, Median and Mode for mixed data
2. Population Variance, Standard deviation and coefficient of variation for mixed data
3. Sample Variance, Standard deviation and coefficient of variation for mixed data

2. Missing frequency for
1. Ungrouped data The Mean of the observations 18,14,15,19,15,a,12,15,16 is 16. Find missing frequency a
2. Grouped data 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

 3. Statistics Word Problem 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.

4. Statistics Graph
1. Histogram
2. Frequency Polygon
3. Frequency Curve
4. Less than type cumulative frequency curve
5. More than type cumulative frequency curve
The frequency distribution of the marks obtained by 100 students 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 number of students 8 15 20 45 12

 5. Arithmetic Mean, Geometric Mean, Harmonic Mean 1. Find Arithmetic mean, Geometric mean, Harmonic mean Find Arithmetic mean, Geometric mean, Harmonic mean for ungrouped data like 2,3,4,5,6 2. Find X from Arithmetic mean, Geometric mean, Harmonic mean Find X where Arithmetic mean=3.5 for ungrouped data 2,3,X,5 3. Find Mean or Median or Mode from other two's Find Mode when Mean=3 and Median=4

6. Combined mean and
combined standard deviation
Find the combined standard deviation from the following data.
 A B number of Observations 40 60 Average 10 15 S.D. 1 2

7. Mean deviation about mean for
1. Ungrouped data 85,96,76,108,85,80,100,85,70,95
2. Grouped data Calculate mean deviation about mean for the following distribution.
 Marks 0-10 10-20 20-30 30-40 40-50 50-60 60-70 No. of student 6 5 8 15 7 6 3

8. Pearson's Correlation Coefficient
1. For X & Y or Class-X & Y
a. Correlation Coefficient r
b. Covariance - Population cov(x,y), Sample cov(x,y)
Calculate correlation coefficient for following weights fathers X and their sons Y
 X 65 66 67 67 68 69 70 72 Y 67 68 65 68 72 72 69 71
2. For bivariate grouped data
a. Correlation Coefficient r
b. Covariance - Population cov(x,y), Sample cov(x,y)
Calculate the correlation coefficient
 Class-YClass-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

9. Spearman's Rank Correlation Coefficient (RHO) 1. Ten participants in a contest are ranked by two judges as follows
 X 1 6 5 10 3 2 4 9 7 8 Y 6 4 9 8 1 2 3 10 5 7
2. 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

10. Regression line equations
1. Find the equation of two regression lines, also estimate Find the equation of regression line equations and correlation coefficient from the following data.
 X 28 41 40 38 35 33 46 32 36 33 Y 30 34 31 34 30 26 28 31 26 31
2. Find Correlation Coefficient from two Regression line equations The regression equation of two variables are 5y = 9x - 22 and 20x = 9y + 350. Find the means of x and y. Also find the value of r.
3. Find Regression line equations using mean, standard deviation and correlation correlation (r) 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 line equations and estimate y for x = 50 and x for y = 30.
4. Find Regression line equations from sum x, sum y, sum x^2, sum y^2, sum xy, n The following information is obtained for two variables x and y. Find the regression equations of y on x.
 sum xy = 3467 sum x = 130 sum x^2 = 2288 n = 10 sum y = 220 sum y^2 = 8822

11. Regression line equations for bivariate grouped data Find Regression Lines
 Class-YClass-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

12. Curve Fitting - Method of Least Squares
1. Fitting a straight line (y=a+bx)
2. Fitting a second degree parabola (y=a+bx+cx^2)
3. Fitting a cubic equation (y=a+bx+cx^2+dx^3)
Fit a straight line, second degree parabola, cubic equation for the following data on production.
 Year 1996 1997 1998 1999 2000 Production 40 50 62 58 60

13. ANOVA - analysis of variance
1. One-way ANOVA
2. Two-way ANOVA
Solve using One-way ANOVA method
 Observation A B C D 1 421 325 320 362 2 118 102 122 56 3 591 518 552 509 4 14 26 20 2 5 116 14 26 46

 14. Distribution tables 1. Normal Distribution(Z) 2. t Distribution 3. Chi square Distribution 4. F Distribution 5. Binomial Distribution

 15. Parametric test 1. F test: 2 sample 2. t test: 1 sample, 2 sample 3. Standard error: 1 sample

 16. Non parametric test 1. Sign test: 1 sample, 2 sample 2. Mann whitney U test: 2 sample 3. Kruskal wallis test: K sample 4. Chi square test: 1 Sample, K Sample 5. Median test: 1 sample, 2 sample 6. Mood's Median test: 2 sample

 17. Permutation & combination 1. Find n! 2. Find (n!)/(m!) 3. Find {::}^nP_r 4. Find {::}^nC_r 5. How many words can be formed from the letters of the word daughter? 6. How many ways a committee of players can be formed ? 7. Permutation, Combination List

 18. Probability 1. Coin 2. Dice 3. Cards 4. Balls