by Selim Bora

1
Business Research Methods

• Lecture 6
• by Selim Bora

2
Graphs

• The distribution of a variable tells us what
  values it takes and how often it takes these
  values.
• To see what data say, start with graphs. Pie
  chart and bar graphs are two illustrative types.
• Pie charts show how a whole is divided into
  parts, where wedges within the circle represent
  the parts, with the angle spanned by each wedge
  in proportion to the size of that part.
• The bar graph make it clear to compare different
  values, where the height of each bar shows
  percentage of each part.

3
Categorical and Quantitative Variables

• A categorical variable places an individual into
  one of several groups or categories.
• A quantitative variable takes numerical values
  for which arithmetic operations such as adding
  and averaging make sense.
• To display distributions of a categorical
  variable, use a pie chart or a bar graph.
• Pie charts always show the parts of some whole,
  but bar graphs can compare any set of numbers
  measured in the same units.
• Pictogram is a bar graph in which pictures
  replace the bars, however the proportion of the
  images must exactly be equal to the proportion of
  the values, therefore tricky.

4
Change Over Time Line Graphs

• To show how a quantitative variable changes over
  time, use a line graph.
• A line graph of a variable plots each observation
  against time at which it was measured.
• Always put time on the horizontal scale of your
  plot and the variable you are measuring on the
  vertical scale.
• Connect the data points by lines to display the
  change over time.
• Line graphs could be stretched or squeezed to
  create a particular impression.

5
Seasonal Variation, Seasonal Adjustment

• Look for an overall pattern.
• A trend is a long-term upward or downward
  movement over time.
• Look for striking deviations(sharp increases or
  decreases) from the overall pattern.
• A pattern that repeats itself at known regular
  intervals of time is called seasonal variation.
• Many series of regular measurements over time are
  seasonally adjusted.
• That is, the expected seasonal variation is
  removed before the data are published.

6
Histograms

• The most common graph of a distribution of a
  quantitative variable is a histogram.
• Divide the range of the data into classes of
  equal width.
• Count the number of individuals in each class.
• Draw the histogram.
• Mark on the horizontal axis the scale for the
  variable whose distribution you are displaying.
• The vertical axis contains the scale of counts.
• Each bar represents a class.
• The base of the bar covers the class, and the bar
  height is the class count.
• Theres no space between the bars unless a class
  is empty, so that its bar height is zero.

7
Interpreting Histograms

• In any graph of data, look for an overall pattern
  and also for striking deviations from that
  pattern.
• An outlier in any graph of data is an individual
  observation that falls outside the overall
  pattern of the graph.
• To describe the overall pattern of a
  distribution
• Give the center and the spread.(Chapter 12)
• See if the distribution has a simple shape that
  you can describe in a few words.

8
Symmetric and Skewed Distributions

• A distribution is symmetric if the right and left
  sides of the histogram are approximately mirror
  images of each other.
• A distribution is skewed to the right if the
  right side of the histogram(containing the half
  of the observations with larger values) extends
  much farther out than the left side. It is skewed
  to the left if the left side of the histogram
  extends much farther out than the right side.

9
Stemplots

• To make a stemplot
• Separate each observation into a stem consisting
  of all but the final(rightmost) digit and a leaf,
  the final digit.
• Stems may have as many digits as needed, but each
  leaf contains only a single digit.
• Write the stems in a vertical column with the
  smallest at the top,, and draw a vertical line at
  the right of this column.
• Write each leaf in the row to the right of its
  stem, in increasing order out from the stem.
• We usually favor stemplots when we have a small
  number of observations and histograms for larger
  data sets.