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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 ClassX & 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`
`= 88`
Median : 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`
`= 85`
Mode : 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 
610 
1020 
2030 
3050 
5070 
70100 
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`=16`
Here `18,14,15,19,15,a,12,15,16`
Here Mean `bar x = 16` and `n = 9`
`sum x_i = 18 + 14 + 15 + 19 + 15 + a + 12 + 15 + 16`
`= a + 124`
Mean `bar x = (sum x_i)/n`
`16 = (a + 124)/9`
`144 = a + 124`
`a = 144  124`
`a = 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 




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 = 10`
`Sigma(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 = 10`
`Sigma 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 
010 
1020 
2030 
3040 
4050 
5060 
6070 
No. of srudent 
6 
5 
8 
15 
7 
6 
3 
2. Calculate mean deviation from median for the following distribution.
Class 
13 
35 
57 
79 
911 
1113 
1315 
1517 
Frequency 
6 
53 
85 
56 
21 
26 
4 
4 
3. Calculate mean deviation from median for the following distribution.
Class 
34.9 
56.9 
78.9 
910.9 
1112.9 
1314.9 
1516.9 
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 
4.512.5 
12.520.5 
20.528.5 
28.536.5 
36.544.5 
44.552.5 
52.560.5 
60.568.5 
68.576.5 
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 
5055 
4550 
4045 
3540 
3035 
3530 
2025 
f 
25 
30 
40 
45 
80 
110 
170 






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 
1314 
200 
124 
1415 
300 
180 
1516 
100 
65 
1617 
50 
34 
1718 
150 
99 
1819 
400 
252 
1920 
250 
145 
2021 
150 
81 
2122 
25 
12 
2223 
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.

90100 
100110 
110120 
120130 
5055 
4 
7 
5 
2 
5560 
6 
10 
7 
4 
6065 
6 
12 
10 
7 
6570 
3 
8 
6 
3 
2. Calculate the correlation coefficient.

18 
19 
20 
21 
350400 
1 
4 
6 
10 
300350 
2 
6 
8 
5 
250300 
3 
5 
4 
2 
200250 
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.

90100 
100110 
110120 
120130 
5055 
4 
7 
5 
2 
5560 
6 
10 
7 
4 
6065 
6 
12 
10 
7 
6570 
3 
8 
6 
3 
2. Calculate the correlation coefficient.

18 
19 
20 
21 
350400 
1 
4 
6 
10 
300350 
2 
6 
8 
5 
250300 
3 
5 
4 
2 
200250 
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
2. Fit a straight line y = a + bx using the following data








