Ricky scored below runs in his last 7 innings 2 runs, 19 runs, 38 runs, 9 runs, 13 runs, 87 runs, 4

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27 Jul 2017 Standard Deviation

Ricky scored below runs in his last 7 innings
2 runs, 19 runs, 38 runs, 9 runs, 13 runs, 87 runs, 49 runs
Find population standard deviation for his score in last 7 innings?

OPtion

1) 27.72
2) 27.32
3) 27.22
4) 27.12
5) 27.52
6) 27.42
7) 27.82
8) 27.62
9) 27.92
10)None of these

Solution

Mean of 7 score = (2+9+38+19+13+87+49)/7 = 217 =31
Sum of squared difference from mean for each number = (31-2)^2 + (31-9)^2 + (31-38)^2 + (31-19)^2 + (31-13)^2 + (31-87)^2 + (31-49)^2
= 7379

Average of Squared difference (Variance) = 7379/7 = 757.43
Population Standard Deviation = Square root of variance = 757.43^1/2 = 27.52

Correct Option: 5 Best Solution (13)

SAYAN CHATTERJEE   7 years AGO

avg. (A)= 1/7*(2+19+38+9+13+87+49)
= 31
sd. = root of (1/7*(summation of (A-x)^2)
= 27.52.
Option 5.

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Mukund Manohar   7 years AGO

Mean of runs of 7 innings = (2+19+38+9+13+87+49)/7 = 217/7 = 31
Sum of squared difference from mean of each number
= (31-2)^2 + (31-19)^2 + (31-38)^2 + (31-9)^2 + (31-13)^2 + (31-87)^2 + (31-49)^2 = 841 + 144 + 49 + 484 + 324 + 3136 + 324 = 5302
Average of squared difference(Variance) = 5302/7 = 757.43
Population Standard Deviation = Sq.root(Variance) = 757.43^(1/2) = 27.52

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Pritam Paul   7 years AGO

Let, the sigma sign '€'
And square '^'
€x= (2+19+38+9+13+87+49)= 217

€x^ = (4+361+1444+81+169+7569+2401)= 12029

n = no.of variants =7

S.d.^ =€x^/n - (€x/7)^
S.d. = 27.52

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AYAN PAUL   7 years AGO

To find the Population Standard deviation first of all we have to find the mean of those given value which is = (217/7)=31
Now we have to find the variance which is [(2-31)^2 + (19-31)^2 + (38-31)^2 + (9-31)^2 + (13-31)^2 + (87-31)^2 + (49-31)^2 ] / 7 = 757.428
Now Population Standard deviation will be (757.428)^1/2 = 27.52

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G.S.Kantharao   7 years AGO

Scores are 2,19,38,9,13,87,49
Average=(2+19+38+9+13+87+49)/7=217/7=31
Square of deviations=[(2-31)^2+(19-31)^2(+(38-31)^2+(9-31)^2+(13-31)^2+(87-31)^2+(49-31)^2]
Average=5302/7=757.428571
Population S.D=√757.428571=27.52
Hence the right option is 5👈.

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KOWSALYA   7 years AGO

mean=(38+2+19+9+13+87+49)/7=31
populationx S.D=√(1/6*((38-31)^2+(2-31)^2+(19-31)^2+(9-31)^2+(13-31)^2+(87-31)^2+(49-31)^2)
=27.52

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abhishek   7 years AGO

Sum of given sample i.e. 2 + 19 + 38 + 9 + 13 + 87 + 49 = 217
Average or Mean is 217/7 = 31
Now Subtract each number with the mean and square it.

(31-2)^2 + (31-19)^2 + (31-38)^2 + (31-9)^2 + (31-13)^2 + (31-87)^2 + (31-49)^2 = 5302

then divide it with total number of samples i.e. 5302/7 = 757.42857

then take the root of above result (757.42857)^0.5 = 27.52
option 5)

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ManikumarSoruvu   7 years AGO

Ans:27.52
Total runs scored by Ricky in 7 Innings=2+19+38+9+13+87+49=217
Mean=217/7=31
Standard Deviation=Sqrt(Variance)
But,
Variance=[(Sum of squares of All the observations)/(Number of observations)]-Square(Mean)
Therefore,
Variance=[(2*2+19*19+38*38+9*9+13*13+87*87+49*49)/7]-31*31=757.4285....
Now ,
Standard Deviation=sqrt(757.4285...)=27.52141...

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kulbir singh   7 years AGO

According to the rules of deviation mean of last 7 scores=217/7=31
Then (1n to7n-mean)²=5302
Then 5302/7=757.42
Then sqrt of 757.42 is approximately equal to 27.52 which is option no. 5

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Ravi   7 years AGO

get the mean of the numbers which will be 31
now subtract 31 from each number get square the number
now take the mean of all numbers after squaring which will be 5302/7=757.42
now it is the variance now take the square root of 757.42 and the answer will be 27.52

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Macharla Ramya   7 years AGO

mean=(2+19+38+9+13+87+49)÷7==31
variance=(xi-(mean)^2)÷7
standard deviation=√variance
SD=√(757.43)

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VARUN   7 years AGO

Mean = 31
DIFFERENSES FROM MEAN=-29,-12,7,-22,-18,56,18
SQUARE OF DIFFERNSES=841,144,49,484,324,3136,324
Sum of differnses=5302
S.D=SQUARE ROOT OF (5302/7)=27.52

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umend   7 years AGO

To calculate standard deviation
1.calculate mean=(2+19+38+9+13+87+49)/7=31
2. subtract each innings run with mean and square it
(31-2)^2=841
(31-19)^2=144 and so on
3.take sum of abv result and divide it by no of innings
(841+144+49+484+324+3136+324)/7=757.428
4.take square root of abv result
=27.52
Ans:27.52

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