SOLUTION: Find the range, standard deviation, and variance of A survey of 10 fast-food restaurant noted the number of calories in a mid-sized hamburger. The following are results 514 507

Question 1158372: Find the range, standard deviation, and variance of
A survey of 10 fast-food restaurant noted the number of calories in a mid-sized hamburger. The following are results
514 507 502 498 496 506 458 478 463 514
Answer by KMST(5396) (Show Source): You can put this solution on YOUR website!
Range, standard deviation, and variance are measures of the dispersion of the data in a set.
A long time ago, in college, I would calculate them using paper and pen, based on their definitions.
Nowadays, a calculator, or computer software can calculate them for us easily, but we have to understand what this measure tell us and exactly what our devices.

Range:
The range is the difference between the smallest and greatest values.

Variance:
The mean (average) of all 10 values is

The deviations from the mean for the individual values are:
(514 appears twice)

Their squares are:
(514 appears twice)

The variance is the average of those squares:

Standard deviation:
The standard deviation, as asked in this question, is the square root of the variance as calculated above:
(rounded)
Software that calculates statistics would have to forms of standard deviation:
the standard deviation of a population, calculated as above, and
the standard deviation of a sample, used to estimate the dispersion of the whole population of data based on a sample of N items. In the second case, the sum of squares in divided by N-1 instead.
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