Percentiles and Box-and- Whisker Plots Definitions Percentiles and Box-and- Whisker Plots

Goals Today Interpret the meaning of percentile scores Compute the median, quartiles, and five-number summary from raw data Make a box-and-whisker plot Interpret the results of a box-and-whisker plot Describe how a box-and-whisker plot indicates spread of data about the median

Definitions Pth Percentile - a value such that P% of the data fall at or below it and (100-P)% of the data fall at or above it.

Definitions Pth Percentile - a value such that P% of the data fall at or below it and (100-P)% of the data fall at or above it. Examples?

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Definitions Quartile - Percentiles that divide the data into fourths First Quartile Q1 is the 25th percentile First Quartile Q2 is the 50th percentile First Quartile Q3 is the 75th percentile Cards

Definitions Calculate Quartile Order the data from smallest to largest Find the median. This is the second quartile The First Quartile Q1 is then the median of the lower half of the data; that is, it is the median of the data falling below the Q2 position (and not including Q2) The third quartile Q3 is the median of the upper half of the data; that is, it is the median of the data falling above the Q2 position (and not including Q2). Cards

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Definitions Interquartile range, (IQR) - Q3 - Q1 Five- Number Summary - Lowest Value Q1 Median Q3 Highest Value Cards

Definitions Box-and-Whisker Plot - A graphic sketch of the data using the five numbers Cards

How to make a box-and-whisker plot Definitions How to make a box-and-whisker plot Draw a vertical scale to include the lowest and highest data values To the right of the scale, draw a box from Q1 to Q3 Include a solid line through the box at the median level Draw vertical lines, called whiskers, from to the lowest value and from Q1 to the highest value Q3 Cards

Pg. 105. 14, 15 Pg. 117. 1, 2, 7

Definitions Population Mean = = Σx/N Population Variance = 2 = Σ(x - )2 / N Population Standard Deviation = = Σ(x - )2 / N Cards

“Quiz” Please calculate the x Median Mode Range S2 S n For the Following set of data: 1, 1, 3, 3, 3, 4

Definitions Coefficient of variation (CV) - The standard deviation as a percentage of the sample or population For a Sample CV = (s / x)*100% For a Population CV = ( / )* 100% Cards

Definitions Chebyshev’s Theorem - For any set of data and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is at least: 1- 1/(k2) Cards

Group Project Get into groups of around 5 Decide a piece of information you want to find Something You can calculate Mean Median Mode Pick a method for collecting your sample Sampling type Time

Group Project (Requirements) Organize your data for me to check (Google Sheets, excel) Data points What is your population? What is your sample? How did you sample? Make a Frequency Distribution Table You pick number of classes Draw a histogram Central Points: Mean, Median, Mode Measurements of Variation: Range, Variance, Standard Deviation, Coefficient of Variation Define your Chebychev intervals 75% 88.9% 93.8% Create a Five-Number Summary (if possible) Draw Box-and-Whisker Plot

Group Project Presentation Communicate your topic Explain topic Display Graphs Powerpoint ELMO Highlight key information Draw conclusions from data Infer something about your population