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.