Question

Cereal. A dietician obtains the amounts of sugar (incentigrams) from 100 centigrams (or 1 gram) in each of 10 differentcereals, including Cheerios, Corn Flakes, Fruit Loops, and 7others. These values are listed below. Is thestandard deviation of those values likely to be a good estimate ofthe standard deviation of the amounts of sugar in each gram ofcereal consumbed by the population of all Americans who eatcereal? Why or why not?

3, 24, 30, 47, 43, 7, 47, 13, 44, 39

Find the range, variance, standard deviation

Answer 1

Range is 44

mean is 29.7

variance is 289.56

standard deviation is 17.016

Explanation:

The data given as follows

3, 24, 30, 47, 43, 7, 47,13, 44, 39

Range = maximum - minimum

= 47 -3 = 44

mean =
`(3+24+30+47+43+7+47+13+44+39)/(10)` = 297/10 = 29.7

variance =
`(sum xi^2 )/(N) - mean^2 }`

= 289.56

SD =
`√(variance)` = 17.016

The standard deviation of the given data is not a good measure as the range and standard deviation are far apart. The standard deviation gives how the given data is dispersed from the mean or expected value, while the range gives a rough idea of variability of the data.