Statistical Methods examples

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Statistical Methods examples (Calculators)

1.1 Ungrouped data

85,96,76,108,85,80,100,85,70,95

1. Mean, Median and Mode for ungrouped data
2. Quartile, Decile, Percentile, Octile, Quintile 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
9. Five number summary for ungrouped data
10. Box and Whisker Plots for ungrouped data
11. Construct an ungrouped frequency distribution table
12. Construct a grouped frequency distribution table
13. Maximum, Minimum for ungrouped data
14. Sum, Length for ungrouped data
15. Range, Mid Range for ungrouped data
16. Stem and leaf plot for ungrouped data
17. Ascending order, Descending order 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. Quartile, Decile, Percentile, Octile, Quintile 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
9. Five number summary for grouped data
10. Box and Whisker Plots for grouped data
11. Mode using Grouping Method for grouped data
12. Less than type Cumulative frequency table for grouped data
13. More than type Cumulative frequency table for grouped data
14. Class and their frequency table 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

1. Mean of the following distribution is 18.1. Find the 1 missing frequency.

Class	5 - 10	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35
f	11	20	35	20	a	6

2. The mean of a frequency distribution of 40 persons is 16.5. Find the 2 missing frequencies.

Class	0 - 5	5 - 10	10 - 15	15 - 20	20 - 25	25 - 30	30 - 35
f	1	7	11	?	?	4	2

3. The median and mode of a frequency distribution of 230 person are 33.50 and 34 respectively. Find the 3 missing frequencies.

Class	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70
f	4	16	?	?	?	6	4

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
6. Ogive (cumulative frequency curve)
7. Frequency polygon with the help of Histogram
8. Frequency curve with the help of Histogram

1. Simple bar graph
2. Multiple bar graph
3. Percentage bar graph
4. Simple stacked bar chart
5. Percentage stacked bar chart
6. Pie Chart
7. Donut Chart
8. Scatter Plot | XY Graph
9. Line Graph

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 Covariance, Sample Covariance

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 Covariance, Sample Covariance

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

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-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

12. Curve Fitting - Method of Least Squares

1. Fitting straight line `(y=a+bx)`
2. Fitting second degree parabola `(y=a+bx+cx^2)`
3. Fitting cubic equation `(y=a+bx+cx^2+dx^3)`
4. Fitting exponential equation `(y=ae^(bx))`
5. Fitting exponential equation `(y=ab^x)`
6. Fitting exponential equation `(y=ax^b)`

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

19. Time Series and Forecasting
1. Simple Moving Average
2. Weighted Moving Average
3. Exponential Moving Average
4. Single Exponential Smoothing
5. Simple Moving Average forecast
6. Weighted Moving Average forecast
7. Exponential Moving Average forecast
8. Single Exponential Smoothing forecast

20. Index Number
1. Fixed base method and Chain base method 2. Unweighted Index Number 3. Fixed base method and Chain base method for bivariate grouped data 4. Conversion of fixed base index numbers into chain base index numbers 5. Weighted Index Numbers 6. Weighted average method 7. Cost of living Index number

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