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Median and Mean: Differences in Data Distribution, Study Guides, Projects, Research of Mathematical Statistics

The University of Mississippi (Ole Miss)Mathematical Statistics

This document compares the median and mean as measures of central tendency in data distribution. It discusses their definitions, differences, and provides examples of uniform distribution with given intervals to calculate percentages of observations falling below, above, and between certain ranges, as well as finding the mean and median.

Typology: Study Guides, Projects, Research

2021/2022

Uploaded on 09/27/2022

yorket
yorket 🇺🇸

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bg1
Median vs Mean
yThe median is the equal areas. It separates
the area in half. 50% on the left, 50% on
the right
yThe mean is the balance point, the point
at which the curve would balance if made
of solid material.
9.
The distribution is skewed to the right so that
the median < mean. The median is approximately
3.5 and the mean is approximately 4.2.
10.
yThe distribution is well approximated by a
uniform distribution between 0 and 9 having
mean=median=4.5.
pf3

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Median vs Mean y The median is the equal areas. It separatesthe area in half. 50% on the left, 50% onthe right y The mean is the balance point, the pointat which the curve would balance if madeof solid material. 9. The distribution is skewed to the right so thatthe median < mean.

The median is approximately 3.5 and the mean is approximately 4.2.

10.^ y^ The distribution is well approximated by auniform distribution between 0 and 9 havingmean=median=4.5.

Uniform Density CurvesRectangular – Area found by length x widthArea must equal 1!

Uniform Distribution with interval 0 to 4What percent of observations fall between 1and 3? What is the mean and median?

Uniform Distribution with interval 0 to 4What percent of observations fall below 1.5?What percent of observations fall above 4.3?

Draw a density curve that is uniform, with awidth of 6. a) What is the mean? The median?