4th Assignment of QBA

7/27/2019 4th Assignment of QBA

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Q No. 01The marks obtained by 9 students are 46, 31,35,45,39,36,41,48 and 36. Find the Range and co-

efficient of Dispersion.

Re-arranging data

31 35 36 36 39 41 45 46 48

Here Maximum Value of X = X m = 48

Minimum value of X = X0 = 31

Range = R = Xm X0

R = 48 31

Co-efficient of Dispersion = C-OD = Xm X0 / Xm + X0

C-OD = 48 31 / 48 + 31

C-OD = 17 / 79

R = 17

C-OD = 0.215


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Q No. 02Find the Quartile deviation and the co-efficient of quartile deviation from following data.

02 04 06 08 10 12

Quartile Deviation = Q.D = Q3 Q1 / 2

Here

Q3 = Value of 3(n + 1 / 4) th item

Q3 = Value of 3(6 + 1 / 4) th item = 5.25

Q3 = 5th

item + 0.5(6th

5th

item)

Q3 = 10 + 0.25(12 10)

Q3 = 10.50

Q1 = Value of (n + 1 / 4) th item

Q1 = Value of (6 + 1 / 4) th item = 1.75

Q1 = 1st item + 0.75(2nd 1st item)

Q1 = 2 + 0.75(4 2)

Q1 = 3.5

Quartile Deviation = Q.D = 10.50 3.5 / 2

Co-efficient of quartile deviation = C-O-Q-D = Q3 Q1 / Q3 + Q1

Co-efficient of quartile deviation = C-O-Q-D = 10.50 3.50 / 10.50 + 3.50

Co-efficient of quartile deviation = C-O-Q-D = 07 / 14

Quartile Deviation = Q.D = 3.5

Co-efficient of quartile deviation = C-O-Q-D = 0.50


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Q No. 03Calculate the Mean deviation from the mean and also calculate the co-efficient of mean

deviation.

X (X-X)32 32-43= -11

33 33-43= -1035 35-43= -836 36-43= -7

41 41-43= -245 45-43= 02

48 48-43= 0551 51-43= 08

54 54-43= 1156 56-43= 13

431 01

Mean = X = X /n

Mean = 431 / 10

Mean = 43.1 or 43

Mean deviation from mean = M.D = (X X) / n

M.D = 01 / 10

Co-efficient of mean deviation = Mean deviation from mean / mean

Co-efficient of mean deviation = 0.1 / 43

M.D = 0.1

Co-efficient of mean deviation =0.002


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Q No. 04A population of N = 10 has the observations 6, 9, 11, 13, 14, 19, 20, 25, 26 and 29. Find its

variance and standard deviation.

X (X-X) (X-X)2

06 06-17= -11 121

09 09-17= -08 6411 11-17= -06 3613 13-17= -04 16

14 14-17= -03 0919 19-17= 02 04

20 20-17= 03 0925 25-17= 08 64

26 26-17= 09 8129 29-17= 12 144

172 02 548

Mean = X = X /n

Mean = 172/ 10

Mean = 17.2 or 17

Variance = 2= (X X) 2 / n

Variance = 2 = 548 / 10

Standard Deviation = = (X X) 2 / n

Standard Deviation = = 10

Standard Deviation = =

Variance = 2 = 54.8

Standard Deviation = = 7.42


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Q No. 05Calculate the variance and standard deviation from the following marks obtained by 11

students.

X (X-X) (X-X)232 32-39= -07 49

33 33-39= -06 3636 36-39= -03 0936 36-39= -03 09

37 37-39= -02 0439 39-39= 00 00

39 39-39= 00 0041 41-39= 02 04

45 45-39= 06 3646 46-39= 07 4948 48-39= 09 81

432 03 277

Mean = X = X /n

Mean = 432/ 11

Mean = 39.27 or 39


Variance = 2 = 277 / 11



Standard Deviation = =

Variance = 2 = 25.11



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Q No. 06Using the co-efficient of variation determines whether or not there is greater variation among

the score of two players.

Afridi (X) (X-X) (X-X)2 Tandolker (X-X) (X-X)2100 100-43= 57 3249 45 45-54= -9 81

00 00-43= -43 1849 55 55-54= 01 0170 70-43= 27 729 50 50-54=-4 1605 05-43= -38 1444 65 65-54= 11 121

40 40-43= -03 09 55 55-54= 01 01

215 0 7280 270 0 220

Mean of Afridi (X) = X = X /n

Mean = 215/ 05

Mean = 43



Co-efficient of variation of Afridi = ( / n 100) %

Co-efficient of variation of Afridi = (38.158 / 05 100) %

Mean of Tandolker (X) = X = X /n

Mean = 270/ 05

Mean = 54


Co-efficient of variation of Afridi = 763.16 %


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Co-efficient of variation of Tandolker = ( / n 100) %

Co-efficient of variation of Tandolker = (6.634 / 05 100) %

Q No. 07Estimate the

1) Range and co-efficient of range.2) Quartile deviation and the co-efficient of quartile deviation.3) Mean deviation and co-efficient of mean deviation.4) Variance5) Standard Deviation6) Co-efficient of variation

From following data2,3,4,5,6,8,10,12,14,16,18,20.

X (X-X) (X-X)22 02-9.83= -7.83 61.31

3 03-9.83= -6.83 46.654 04-9.83= -5.83 33.99

5 05-9.83= -4.83 23.33

6 06-9.83= -3.83 14.698 08-9.83= -1.83 03.35

10 10-9.83= 0.17 00.03

12 12-9.83= 2.17 04.7114 14-9.83= 4.17 17.30

16 16-9.83= 6.17 38.0718 18-9.83= 8.17 66.75

20 20-9.83= 10.17 103.43

118 0.04 413.56


Co-efficient of variation of Tandolker = 132.66


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Mean = X = X /n

Mean = 118/ 12

Mean = 9.83

1- Range and co-efficient of range

Here Maximum Value of X = X m = 20

Minimum value of X = X0 = 02

Range = R = Xm X0

R = 20 02

1)Co-efficient of Dispersion = C-OD = Xm X0 / Xm + X0

C-OD = 20 02 / 20 + 02

C-OD = 18 / 22

2)

2- Mean deviation and co-efficient of mean deviation

Mean deviation from mean = M.D = (X X) / n

M.D = 0.04 / 12

Co-efficient of mean deviation = Mean deviation from mean / mean

Co-efficient of mean deviation = 0.0032 / 9.83

R = 18

C-OD = 0.818

M.D = 0.0032

Co-efficient of mean deviation =0.0003


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3- Variance


Variance = 2 = 413.56 / 12

4-Standard Deviation



5-Co-efficient of variation

Co-efficient of variation = ( / n 100) %

Co-efficient of variation = (5.87 / 12 100) %

6-Quartile deviation and the co-efficient of quartile deviation


Here

Q3 = Value of 3(n + 1 / 4) th items

Q3 = Value of 3(12 + 1 / 4) th item = 9.75

Q3 = 9th item + 0.75(10th 9th item)

Q3 = 14 + 0.25(16 14)

Q3 = 15

Variance = 2 = 34.46


Co-efficient of variation of Tandolker = 48.92


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Q1 = Value of (n + 1 / 4) th item

Q1 = Value of (12 + 1 / 4) th item = 3.25

Q1 = 3st item + 0.25(4nd 3rd item)

Q1 = 4 + 0.25(5 4)

Q1 = 4.25

Quartile Deviation = Q.D = 15 4.25 / 2

Co-efficient of quartile deviation = C-O-Q-D = Q3 Q1 / Q3 + Q1

Co-efficient of quartile deviation = C-O-Q-D = 15 4.25 / 15 + 4.25

Co-efficient of quartile deviation = C-O-Q-D = 10.75 / 19.25

Q No. 08

1-Dispersion

A quantifiable variation of measurements of differing members of a population.

2- Absolute Measure of Dispersion

These measures give us an idea about the amount of dispersion in a set of observations. They

give the answers in the same units as the units of the original observations. When the

observations are in kilograms, the absolute measure is also in kilograms.

The Range

The Quartile Deviation

The Mean Deviation

The Standard deviation and Variance

Quartile Deviation = Q.D = 5.38

Co-efficient of quartile deviation = C-O-Q-D = 0.561


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Relative Measure of Dispersion

These measures are calculated for the comparison of dispersion in two or more than two sets

of observations. These measures are free of the units in which the original data is measured. If

the original data is in dollar or kilometers, we do not use these units with relative measure ofdispersion. These measures are a sort of ratio and are called coefficients.

Coefficient of Range or Coefficient of Dispersion.

Coefficient of Quartile Deviation or Quartile Coefficient of Dispersion.

Coefficient of Mean Deviation or Mean Deviation of Dispersion.

Coefficient of Standard Deviation or Standard Coefficient of Dispersion.

Coefficient of Variation

3-The Range

Range is defined as the difference between the maximum and the minimum observation of the

given data. If denotes the maximum observation denotes the minimum observation

then the range is defined as

Range

4-Quartile Deviation

It is based on the lower quartile and the upper quartile . The difference is

called the inter quartile range. The difference divided by is called semi-inter-quartile range or the quartile deviation. Thus


The quartile deviation is a slightly better measure of absolute dispersion than the range.

5-Mean Deviation

The mean of the absolute deviations of observations from some suitable average which may be

the arithmetic mean, the median or the mode. The difference is called deviation and when we

ignore the negative sign, this deviation is written as { (X X) / n}.


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6-The Variance

Variance is defined as the average of the squared difference between each of the observations in a set of data

and the mean. For a sample data the variance is denoted is denoted by .

7-Standard Deviation

The standard deviation is defined as the positive square root of the mean of the square deviations taken from

arithmetic mean of the data.


8-Coefficient of VariationWhen we divide mean by standard deviation of give data and multiplied by 100, then this is called

Coefficient of Variation. Formula of Coefficient of Variation is given below,

Co-efficient of variation = ( / n 100) %

4th Assignment of QBA

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