1 Graphing options for Quantitative DataSection 2.2 Graphing options for Quantitative Data

2 Which Graph? Dot-plot and stem-and-leaf plot: HistogramMore useful for small data sets Data values are retained Histogram More useful for large data sets Most compact display More flexibility in defining intervals

3 Dot Plots Dot Plots are used for summarizing a quantitative variableTo construct a dot plot Draw a horizontal line Label it with the name of the variable Mark regular values of the variable on it For each observation, place a dot above its value on the number line

4 Dot plot Example Sodium Data: 11 12 15 22 23 25 31 35 38 42 44 45 4748 52 53

5 Stem-and-leaf plots Stem-and-leaf plots are used for summarizing quantitative variables Separate each observation into a stem (first part of the number) and a leaf (typically the last digit of the number) Write the stems in a vertical column ordered from smallest to largest, including empty stems; draw a vertical line to the right of the stems Write each leaf in the row to the right of its stem; order leaves if desired

6 Stem-and-Leaf Plot ExampleData: 11 12 15 22 23 25 31 35 38 42 44 45 47 48 52 53

7 Histograms A Histogram is a graph that uses bars to portray the frequencies or the relative frequencies of the possible outcomes for a quantitative variable

8 Steps for Constructing a HistogramDivide the range of the data into intervals of equal width Count the number of observations in each interval, creating a frequency table On the horizontal axis, label the values or the endpoints of the intervals. Draw a bar over each value or interval with height equal to its frequency (or percentage), values of which are marked on the vertical axis. Label and title appropriately

9 Learning Objective 4: Histogram for Sodium in CerealsData: 11 12 15 22 23 25 31 35 38 42 44 45 47 48 52 53

10 Try your Quantitative data:

11 Interpreting HistogramsOverall pattern consists of center, spread, and shape Assess where a distribution is centered. Assess the spread of a distribution. Shape of a distribution: roughly symmetric, skewed to the right, or skewed to the left

12 Shape Symmetric Distributions: if both left and right sides of the histogram are mirror images of each other A distribution is skewed to the left if the left tail is longer than the right tail A distribution is skewed to the right if the right tail is longer than the left tail

13 Examples of Skewness

14 Shape and Skewness Consider a data set containing IQ scores for the general public: What shape would you expect a histogram of this data set to have? Symmetric Skewed to the left Skewed to the right Bimodal

15 Shape and Skewness Consider a data set of the scores of students on a very easy exam in which most score very well but a few score very poorly: What shape would you expect a histogram of this data set to have? Symmetric Skewed to the left Skewed to the right Bimodal

16 Questions