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21 Apr 2017, 01:27
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There are a lot of products. Is the standard deviation of the prices of the products less than $60?
1) The median value of their price is $100
2) The range of their price is $110
1) The median value of their price is $100
2) The range of their price is $110
21 Apr 2017, 20:56
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I am Not sure whether i am Right....There a rule suggesting STD Should be approximately equal to One fourth the value of the range...
Here Range is 110 So STD will be less than 60...
statement 1 tells next to nothing..
Hence B
Here Range is 110 So STD will be less than 60...
statement 1 tells next to nothing..
Hence B
21 Apr 2017, 23:58
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VyshakhR1995
Hi VyshakhR1995,
To be precise Standard deviation of any data set will always be less than equal to Range/2.
I'll demonstrate it with a small example.
consider two numbers 6 and 10.
1. Find the mean. (6+10)/2 = 8
2. Take the difference from the mean. 8 - 6 = 2 , 10 - 8 = -2
3. Square the difference. 2^2 = 4, (-2)^2 = 4
4. Take the mean of the squares of the difference from the mean. => (4+ 4)/2 = 4
5. Take the square root of step 4 result. => \(\sqrt{4} = 2\)
Standard deviation = 2
Range = 10 - 6 = 4 .
In this case, SD is equal to Range/2.
But if you insert any other element within this range, then SD will further decrease.
=> Standard deviation <= Range/2
Thanks.
