Standard Deviation

Is the standard deviation of set of measurements x1, x2, x3, x4,…, x20 less than 3? What is Standard Deviation?

1) The variance for the set of measurements is 4.
2) For each measurement, the difference between the mean and that measurement is 2.

In determining the standard deviation, the difference between each measurement and the mean is squared (the variance), and then the differences are added and divided by the number of measurements. The positive square root of the number is the standard deviation.

1) If each variance is 4, then the sum of all the variances is 4 • 20 = 80. Then ?80 / ?20 = ?4 = 2, which is less than 3; SUFFICIENT
x1 = 4? Is this correct?
x2 = 8?
x3 = 12?
x4 = 16?
X10 = 40?
x20 = 80?

2) For each measurement, the difference between the mean and that measurement is 2. Therefore, the square of each difference is 4, and the calculations then proceed as above; SUFFICIENT

Answer: D

Jackie9988 said:

Is the standard deviation of set of measurements x1, x2, x3, x4,…, x20 less than 3?

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The value of the standard deviation will depend entirely upon the data points. There's no one standard deviation for all data sets. Sorry!

Jackie9988 said:

What is Standard Deviation?

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This should have been covered in class and in your text. Since it wasn't (apparently), you'll need some lessons. We can't provide those lessons here, of course, so please consider some of the many great lessons available online:

. . . . .Google results for "standard deviation"

Jackie9988 said:

1) The variance for the set of measurements is 4.

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Then, by definition (as you'll learn), the standard deviation for this particular set of measurements is "sigma" = sqrt[4] = 2. :wink:

Jackie9988 said:

2) For each measurement, the difference between the mean and that measurement is 2.

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Okay, but... What are you supposed to do with statements (exercises?) (1) and (2)? :?:

Jackie9988 said:

1) If each variance is 4, then the sum of all the variances is 4 • 20 = 80. Then ?80 / ?20 = ?4 = 2, which is less than 3; SUFFICIENT
x1 = 4? Is this correct?
x2 = 8?
x3 = 12?
x4 = 16?
X10 = 40?
x20 = 80?

2) For each measurement, the difference between the mean and that measurement is 2. Therefore, the square of each difference is 4, and the calculations then proceed as above; SUFFICIENT

Answer: D

Click to expand...

I'm sorry, but I have no idea what this means...? :shock:

What is "Answer: D"? What is the meaning of the x[sub:2kgpym8m]i[/sub:2kgpym8m]-values, with their numbers and question-marks? What does "SUFFICIENT" mean in this context?

Please reply with clarification. Thank you!

Eliz.