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1.

Coefficient of standard deviation is:A. `(MD_(barx))/(barX)`B. `(MD_(m))/(M)`C. `(MD_(Z))/(Z)`D. all of these

Answer» Correct Answer - A
A
Discussion
2.

…………………. Is the arithmetic average of the deviations of all the values taken from some average value of the series, ignoring signs of the deviations. (Mean Deviation/Standard Deviation)

Answer» Correct Answer - Mean Deviation
Mean Deviation
Discussion
3.

Two sample of size 100 and 150 respectively have means 15 and 16 and standard deviations 3 and 4 respectively. Find the combined mean and standard deviation of Size 250.

Answer» Given: `N_(1)`=100, `barX_(1)`=15, `sigma_(1)`=3
`N_(2)`=150, `barX_(2)`=16, `sigma_(2)`=4
Now,
`barX_(12)=(N_(1)barX_(1)+N_(2)barX_(2))/(N_(1)+N_(2))`
`=(100xx15+150xx16)/(100+150)`
`=(1,500+2,400)/(250)=(3,900)/(250)=15.6`
`d_(1)=barX_(1)-barX_(12)=15-15.6=-0.6`
`d_(2)=barX_(2)-barX_(12)=16-15.6=0.4`
`sigma_(12)=sqrt(N_(1)sigma_(1)^(2)+N_(2)sigma_(2)^(2)+N_(1)d_(1)^(2)+N_(2)d_(2)^(2))/(N_(1)+N_(2))`
`=sqrt(100xx(3)^(2)+150xx(4)^(2)+100xx(-0.6)^(2)+150xx(0.4)^(2))/(100+150)`
`=sqrt(100xx9+150xx16+100xx0.36+150xx0.16)/(250)`
`=sqrt((900+2,400+36+24)/(250))`
`=sqrt((3,360)/(250))=sqrt(13.44)`
3.67
Hence, the combined mean is 15.6 and combined standard deviation is 3.67.
Discussion
4.

Find out the range and coefficient of range from the following data: 6,12,30,24,45,52,40

Answer» Here, L=6, H=52
Range (R )=H-L
=52-6
=46
Coefficient of Range (CR)`=(H-L)/(H+L)`
`=(52-6)/(52+6)=(46)/(58)`
=0.79
Discussion
5.

`sigma=sqrt((N_(1)sigma_(1)^(2)+N_(2)sigma_(2)^(2)+N_(1)d_(1)^(2)+N_(2)d_(2)^(2))/(N_(1)+N_(2)))` is the formula of:A. combined mean deviationB. combined quartile deviationC. combined standard deviationD. coefficient of variation

Answer» Correct Answer - C
C
Discussion
6.

Mean deviation can be calculation by using:A. meanB. modeC. medianD. all of these

Answer» Correct Answer - D
D
Discussion
7.

Which is the following formulae is used to find out inter quartile range?A. `(Q_(1)-Q_(3))/(2)`B. `(Q_(1)+Q_(3))/(2)`C. `Q_(1)-Q_(3)`D. `Q_(1)+Q_(3)`

Answer» Correct Answer - C
C
Discussion
8.

Range is estimated as the ………………………. Of highest and lowest values of the series. (difference/multiplicatin)

Answer» Correct Answer - difference
difference
Discussion
9.

Coefficient of range is:A. `((H+L)/(H-L))xx2`B. `(H+L)/(2)`C. `(H+L)/(H-L)`D. `(H-L)/(H+L)`

Answer» Correct Answer - D
D
Discussion
10.

Difference between third quartile and first quartile of a series, is called …………….. (Quartile Deviation/Inter Quartile Range)

Answer» Correct Answer - Inter Quartile Range
Inter Quartile Range
Discussion
11.

Two sample of size 100 and 150 respectively have means 50 and 60 deviation of the combined sample of size 250.

Answer» `{:("Given":,N_(1)=100",",barX_(1)=50",",sigma_(1)=5),(,N_(2)=150",",barX_(2)=60",",sigma_(2)=6):}`
Now,
`barX_(12)=(N_(1)barX_(1)+N_(2)barX_(2))/(N_(1)+N_(2))`
`=(100xx50+150xx60)/(100+150)=(5,000+9,000)/(250)`
`(14,000)/(250)=56`
`d_(1)=barX_(1)-barX_(12)=50-56=-6`
`d_(2)=barX_(2)-barX_(12)=60-56=+4`
`sigma_(12)=sqrt((N_(1)sigma_(1)^(2)+N_(2)sigma_(2)^(2)+N_(1)d_(1)^(2)+N_(2)D_(2)^(2))/(N_(1)+N_(2)))`
`=sqrt((100xx(5)^(2)+150xx(6)^(2)+100xx(-6)^(2)+150xx(4)^(2))/(100+150))`
`=sqrt((100xx25+150xx36+100xx36+150xx16)/(250))`
`=sqrt((2,500+5,400+3,600+2,400)/(250))=sqrt((13,900)/(250))`
`=sqrt(55.6)=7.46`
Hence, the Combined Mean =56 and the Combined Standard Deviation=7.46.
Discussion
12.

Which of the following equations is correct?A. Variance=`sigma`B. Variance=`sigma^(2)`C. Variance=`sigma^(4)`D. Variance=`sqrt(sigma)xx2`

Answer» Correct Answer - B
B
Discussion
13.

Coefficient of variation is a percentage expression of:A. Mean deviationB. quartile deviationC. standard deviationD. None of these

Answer» Correct Answer - C
C
Discussion
14.

Which is the relative measure of dispersion?A. RangeB. Mean deviationC. Coefficient of standard deviationD. None of these

Answer» Correct Answer - C
C
Discussion
15.

………………… measure of dispersion is known as coefficient of dispersion. (Absolute/Relative)

Answer» Correct Answer - Relative
Relative
Discussion
16.

If sum of aquares of items =2,430, arithmctic mean =7, and number of items=12, find the coefficient of variation.

Answer» Given: `sumX^(2)=2,430, barX=7`, N=12
`sigma=sqrt((sumX)/(N)-(barx)^(2))`
`=sqrt((2,430)/(12)-(7)^(2))=sqrt(202.5-49)`
`=sqrt(153.5)=12.39`
`CV=(sigma)/(barX)xx100`
`=(12.39)/(7)xx100=177`
Coefficient of Variation =1.77.
Discussion
17.

If the mean and standard deviation of 75 observations is 40 and 8 respectively, find the new mean and standard deviation if (i) each observation is multiplied by 5. (ii) 7 is added to each observation.

Answer» Given: `barX=40,sigma=8, N=75`
(i) A "change of scale" affects the value of both `barX` and `sigma`. A change of scale occurs when each observation is multiplied by a constant. As a result to that, `barX` and `sigma` also get multiplied by that constant.
Hence,
New `barX="Old "barXxx5`
`=40xx5`
=200
and,
New `sigma="Old "sigmaxx5`
`=8xx5`
=40
(ii) A "change of origin " affects the value of `barX` but not that of `sigma`. A change of origin occurs when eachobservation is increased by a constant .As a result to that, `barX` also increases by the same constant, while `sigma` remains unchanged.
In our question, that constant is 7.
Hence,
New`barX="Old "barX+7`
`=40+7`
=47
While,
New `sigma="Old "sigma`
=8
Discussion
18.

Coefficient of standard deviation is a ……………….. Measure of the dispersion of series. (absolute/relative)

Answer» Correct Answer - relative
relative
Discussion
19.

The coefficient of variation of a series is 58. The standard deviation is 21.2. What is the arithmetic mean?

Answer» Given: CV=58,`sigma`=21.2
`CV=(sigma)/(X)xx100`
`implies " " barX=(21.2)/(58)xx100`
Substituting the values, we get
`barX=(21.2)/(58)xx100=36.6`
Arithmetic Mean=36.6
Discussion