# Example find the mean of the following sample 70 85 a

• Notes
• nrfry
• 23

This preview shows page 6 - 12 out of 23 pages.

ExampleFind the mean of the following sample100,94,78,70,85.
6 / 1
DefinitionThemean from a frequency distributionisx=(f.x)f,wherefis the frequency andxis its corresponding class midpoint.RemarkIf you no longer have the original data values, you can not get the exact valueof the mean. The above one is, in fact, just an estimate. So, you assume thatall values in each class are equal to the class midpoint.ExampleConsider the following frequency table and find the mean.ClassFrequency (f)0-627-13314-20121-27428-342A. Bourhim (Syracuse University)Measures of CenterMAT121, Spring 20157 / 1
Weighted meanWhen data values are assigned different weights, we can compute aweightedmean:x=(w.x)w,wherewis the weight of the data valuex.ExampleFind the final grade if a MAT121 student getsTestGrade (x)Weight(w)Test19515%Test28015%Test39015%Test410015%lab9020%final exam8020%A. Bourhim (Syracuse University)Measures of CenterMAT121, Spring 20158 / 1
Measures of VariationIn this section, we learn about range, standard deviation, and variance. Thesedescribe how far the data values from the mean.RangeRange=maximum value - minimum value.The range is very easy to compute but not very useful.Sample Standard Deviation Formulas=s(x-x)2n-1ORs=vuuuutn(x2)-x2n(n-1).The variance of a sample iss2,the square of the standard deviation. Note that bothsands2are statistics.A. Bourhim (Syracuse University)Measures of CenterMAT121, Spring 20159 / 1
ExampleConsider the following sample1,4,5,2,4,and finds.A. Bourhim (Syracuse University)Measures of CenterMAT121, Spring 201510 / 1