3.1 Frequency Tables 1 Can't Type? press F11 or F5 Can’t Hear? Check: Speakers, Volume or Re-Enter. Put "?" in front of Questions so it is easier to see them.

Definitions A piece of data is a single response to an experiment. The distribution of a variable refers to the way its values are spread over all possible values. A frequency distribution is a listing of observed values and the corresponding frequency of occurrence of each value. Category, Class, Class Interval, or bin is how the data is sorted or recorded. It may be a single item or it may be a group/interval. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 2

Frequency is how often the data occurs. Tally (optional) sometimes used to make it easier to sort the data. Total (row) is the total of each column. Cumulative Frequency is the sum of the data to that row, so the last data row should have the same value as the Total row. Relative Frequency of a row is the percent of that row compared to all the data. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 3

Example The number of pets per family is recorded for 30 families surveyed. Construct a frequency distribution of the following data: Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 4 # of Pets TallyFreq

Pet Example, Con’t. CategoryFrequencyRelative FrequencyCumulative Frequency Total30 Can't Type? press F11 or F5 Can’t Hear? Check: Speakers, Volume or Re-Enter. Put "?" in front of Questions so it is easier to see them. 5

Example The following set of data represents the distance, in miles, that 15 randomly selected second grade students live from school. Construct a frequency distribution with the first class Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 6

Solution Rearrange the data from lowest to highest Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them – 2.0 Frequency # of miles from school Total

Walking Dist. Example, Con’t. CategoryFrequencyRelative FrequencyCumulative Frequency 0.0 – – – – – Total15 Can't Type? press F11 or F5 Can’t Hear? Check: Speakers, Volume or Re-Enter. Put "?" in front of Questions so it is easier to see them. 8

3.2 Picturing Distributions of Data Page 99 Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 9

Definitions of Graphs Bar Chart: the data is across the bottom & frequency is up the side, though it can also be switched, often with gaps between the columns. – Dot Plot: shows the frequency with the number of dots in the column. – Pictograph: can be a dot plot, but with pictures instead of dots. It is any graph that has pictures in it. – Pareto Chart: the columns are sorted by frequency. – Histogram: is a Bar Chart squished together. Line Graph, Line Chart, or Frequency Polygon: is a line graph with observed values on its horizontal scale and frequencies on it vertical scale. – Time Series Diagram: the horizontal is the time. Stem and Leaf Plot has details in the video (if time at end of seminar): Pie Charts: compare parts of one or more components of the whole to the whole. 10

Can't Type? press F11 or F5 Can’t Hear? Check: Speakers, Volume or Re-Enter. Put "?" in front of Questions so it is easier to see them. 11

Histogram, example Frequency # of pets Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 12

Frequency Polygon, example Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them Frequency # of pets

Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 14 Histogram & Frequency Polygon Compared

Example According to a recent hospital survey of 200 patients the following table indicates how often hospitals used four different kinds of painkillers. Use the information to construct a circle graph illustrating the percent each painkiller was used Other 16Acetaminophen 104Ibuprofen 56Aspirin Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 15

Solution Determine the measure of the corresponding central angle Number of Patients 100% Percent of Total 360 degrees 0.12 x 360 = 43.2 degrees 0.08 x 360 = 28.8 degrees 0.52 x 360 = degrees 0.28 x 360 = degrees Measure of Central Angle Total Other Acetaminophen Ibuprofen Aspirin Painkiller Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 16

Solution continued Use a protractor to construct a circle graph and label it properly. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 17

Can't Type? press F11 or F5 Can’t Hear? Check: Speakers, Volume or Re-Enter. Put "?" in front of Questions so it is easier to see them. 18 StatCrunch Graphics

3.3 Graphics in the Media Page 112 Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 19

Some Special Graphs Can't Type? press F11 or F5 Can’t Hear? Check: Speakers, Volume or Re-Enter. Put "?" in front of Questions so it is easier to see them. 20

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3.4 A Few Cautions About Graphics Page 125 Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 22

What is ‘wrong’ with these? Can't Type? press F11 or F5 Can’t Hear? Check: Speakers, Volume or Re-Enter. Put "?" in front of Questions so it is easier to see them. 23 Homes with Cable TV 18 million homes 73 million homes

Which is the better investment & why? Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 24

Stem-and-Leaf Display A stem-and-leaf display is a tool that organizes and groups the data while allowing us to see the actual values that make up the data. – The left group of digits is called the stem. – The right group of digits is called the leaf. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 25

Example The table below indicates the number of miles 20 workers have to drive to work. Construct a stem-and-leaf display Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 26

Solution DataStem-and-Leaf Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put ? in front of Questions so it is easier to see them. 27