Graphical Displays of Information Chapter 3.1 – Tools for Analyzing Data Mathematics of Data Management (Nelson) MDM 4U

Histograms Show:  Continuous data grouped in class intervals  How data is spread over a range Bin width = width of each bar Different bin widths produce different shaped distributions Bin widths should be equal Usually 5-6 bins

Histogram Example These histograms represent the same data One shows much less of the structure of the data Too many bins (bin width too small) is also a problem

Histogram Applet – Old Faithful m.html

Bin Width Calculation Bin width = (range) ÷ (number of intervals)  where range = (max) – (min)  Number of intervals is usually 5-6 Bins should not overlap  wrong: 0-10, 10-20, 20-30, 30-40, etc. Discrete  correct: 0-10, 11-20, 21-30, 31-40, etc.  correct: , , , etc. Continuous  correct: 0-9.9, , , , etc.  correct: , , , , etc.

Mound-shaped distribution The middle interval(s) have the greatest frequency (i.e. the tallest bars) The bars get shorter as you move out to the edges. E.g. roll 2 dice 75 times

U-shaped distribution  Lowest frequency in the centre, higher towards the outside  E.g. height of a combined grade 1 and 6 class

Uniform distribution  All bars are approximately the same height  e.g. roll a die 50 times

Symmetric distribution  A distribution that is the same on either side of the centre  U-Shaped, Uniform and Mound-shaped Distributions are symmetric

Skewed distribution (left or right) Highest frequencies at one end Left-skewed drops off to the left E.g. the years on a handful of quarters

MSIP / Homework Define in your notes:  Frequency distribution (p )  Cumulative frequency (p. 148)  Relative frequency (p. 148) Complete p. 146 #1, 2, 4, 9, 11 (data in Excel file on wiki),13