Age of 4 members in a family are: 2 years, 6 years, 8 years and 16 years. What is the population st

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16 Aug 2017 Standard Deviation

Age of 4 members in a family are: 2 years, 6 years, 8 years and 16 years.
What is the population standard deviation of their ages?

OPtion

1) 4.00
2) 4.39
3) 5.00
4) 5.89
5) 5.39
6) 5.09
7) 4.81
8) 5.99
9) 5.81
10)None of these

Solution

Mean of 4 ages = (2+6+8+16)/32 = 8
Sum of squared difference from mean for each number = (8-2)^2 + (8-6)^2 + (8-8)^2 + (8-16)^2
= 36+4+0+64 = 104

Average of Squared difference (Variance) = 104/4 = 26
Population Standard Deviation = Square root of variance = 26^1/2 = 5.09

Correct Option: 6 Best Solution (14)

G.S.Kantharao   7 years AGO

Mean of avea=(2+6+8+16)/4=8
Sum of the square=(2-8)^2+(6-8)^2+(8-8)^2+(16-8)^2/4
=36+4+0+64/4=26
Popular ion SD=√26=5.09
Hence the Right option is 6👈

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Mukund Manohar   7 years AGO

Mean of 4 ages = (2+6+8+16)/4 = 8
Sum of squared difference from mean for each number = (8-2)^2 + (8-6)^2 + (8-8)^2 + (8-16)^2 = 36 + 4 + 0 + 64 = 104
Average of Squared Difference(Variance) = 104/4 = 26
Population Standard Deviation = Square Root of Variance = 26^(1/2) = 5.09

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SAYAN CHATTERJEE   7 years AGO

mean= 1/4*(6+2+8+16)
= 8
sd=(1/4*((8-6)^2+(8-2)^2+(8-8)^2+(16-8)^2)
= 5.09.
Option 6.

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Ravi   7 years AGO

2+6+8+16/4=8 now 8-2=6,8-6=2,8-8=0 and 8-16=-8 so (6)^2+2^2+0^2+8^2/4
which will be 26 now take square root of 26
√26=5.09

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Varun   7 years AGO

Standard deviation is how much the value as been deviated from the nominal value(average value), so every value is subtracted with the average value, but by doing so, it will give both positive deviations. But we are interested only in deviation,whether positive(to the right) or negative(to the left), so, what we do is square the differences and find its mean, and then take out the applied square back.

Here, it is :
Mean initially = (2+6+8+16)/4 = 8
Therefore deviations = -6 -2 0 +8
Squaring : 36 4 0 64
Summation = 104
Mean now =104/4 = 26
Taking back the applied square = Root ( 26 ) = 5 .099

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Bodla Anupriya   7 years AGO

variance=E(x^2)-E(x)^2=(4+6=36+64+256)/4-(2+6+8+16/4)^2=
90-64=26
standard deviation=√26=5.09

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Vishwas   7 years AGO

firstly calculate the mean=(2+6+8+16)/4=8
subtract each of them with their mean and square the result
result will be 36,4,0,64
Again find the mean of them
Mean=26
Standard Deviation=square_root(26)=5.09

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Divya Batra   7 years AGO

we will use simple formula to calculate population standard deviation.

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AYAN PAUL   7 years AGO

Mean of those ages is = (2+6+8+16)/4 = 8
Now we have to find the squared difference of mean and the all values i.e. (8-2)^2 = 36 , (8-6)^2 = 4, (8-8)^2 = 0, (16-8)^2 = 64
now mean value of these squared difference is = (36+64+4)/4 = 26
now square root of 26 will be equal to = 5.09

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prasanna   7 years AGO

We know that to calculate standard deviation
1.find mean of all numbers
2.substract the mean from number and find square of it
3.find mean of these squared numbers
4.take square root of that number
Thats all we get population standard deviation of ages

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shail   7 years AGO

sd is nothing but deviation to mean of each data point , take values 2,6,8,16 and daviation is -6,-2,0,8
for stdd deviation take squares and add then decide by total no of data points .that's called variance
take it's sqr root to obtain sttdd deviation

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AMAN RASTOGI   7 years AGO

mean 8
mean minus each number square divide by n and square rooting it ..will provide the same

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palak Jain   7 years AGO

1.Mean =2+6+8+16/4=8
2. 6^2+2^2+0^2+8^2/4=104/4=26
3 under root of 26=5.099

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shreya   7 years AGO

mean= 8
2-8=-6.......16-8=8
36+4+64/4=26
√26=5.09

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