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4.1 Measures of Center
We are learning to…analyze how adding another piece
of data can affect the measures of center and spread.
Mean

Mean:

A measure of center, also known as
average.

Mean is the sum of a set of data
divided by the number of data
items.
Median

Median:

A measure of center, that tells the middle number
in a set of data.

If there is no single middle item, the number
halfway between the two data items closest to the
middle is the median.

Basically…just find the mean of the two middle
numbers.
Mode

Mode:

A measure of center for a set of data that tells the
item(s) that appear most often in data set.

There can be no mode.

There can also be more than one mode
Range

Range:

A measure of spread.

The difference (subtraction) between the
greatest data value and least value in a data set.
Standard Deviation
Standard Deviation shows the variation
in data. If the data is close together, the
standard deviation will be small. If the
data is spread out, the standard deviation
will be large.
Standard Deviation of the sample is denoted by the symbol, Sx .
Standard Deviation of the population is denoted by the lowercase
Greek letter sigma,  .
Shape of Data : SKEW
Skewed Left
Symmetric
Skewed Right
Unimodal
Bimodal
Normal: Symmetric
AND Unimodal
Mean compared to Median:
Mean follows the SKEW

When mean is larger than the median, then the
data is:

When mean is smaller than the median, then the
data is:

If the data is skewed left, then the mean is:

If the data is skewed right, then the mean is:
So what do we do with
skewed data?

When data is symmetric, we can use either the
mean or the median to describe the center.

The more skewed the data, the less descriptive is
the mean, since it is affected by the skew. We
would choose the median to describe center,
since the median is resistant to the skew.