Chapter 12, Part 1 STA 200 Summer I 2011

Measures of Center and Spread Measures of Center: – median – mean Measures of Spread: – quartiles & five number summary – standard deviation

Median The median is the midpoint of a distribution. In other words, it’s the number such that half of the observations are smaller and the other half are larger.

Calculating the Median

Example From 1991 to 1999, the total precipitation in Lexington was, to the nearest inch: Find the median. ’91’92’93’94’95’96’97’98’

Another Example In the first 16 days of May 2011, the recorded high temperatures in Lexington were: Find the median. 5/15/25/35/45/55/65/75/ /95/105/115/125/135/145/155/

Quartiles The quartiles help to give the spread of a distribution. If the median is used to measure center, the quartiles should be used to measure spread. There are two of them: the first quartile and the third quartile. The quartiles (along with the median) divide the observations into quarters.

Calculating the Quartiles Put the observations in order, and determine the median. The first quartile (Q 1 ) is the median of the observations less than the overall median. The first quartile will be above 25% of the data. The third quartile (Q 3 ) is the median of the observations greater than the overall median. The third quartile will be above 75% of the data.

Precipitation Example Find the first and third quartiles for the precipitation data:

Temperature Example Find the first and third quartiles for the temperature data:

Five Number Summary & Box Plot In order to get a good idea of the distribution (center and spread), we use what is called a five number summary, and construct a graph called a box plot.

Five Number Summary The five-number summary consists of the median, quartiles, and the largest and smallest observations. These are typically written out in increasing order: minQ 1 MQ 3 max (Note: M = median)

Box Plot The box plot (or box-and-whisker plot) is a graph of the five number summary. How to construct a box plot: – a box extends from the first quartile to the third quartile – a line in the box marks the median – lines extend from the sides of the box to the smallest and largest observations

Precipitation Example For the precipitation data, determine the five number summary and construct a box plot.

Temperature Example For the temperature data, determine the five number summary and construct a box plot.