2.3 Displaying Quantitative Data

Question 1

Stem Plot (stem and leaf plot)

Answer 1

represent numerical data, the stem consists of all the digits except for the right-most digit, leaf consists of the right-most digit, can split and have multiple stems

Question 2

Stem Plot Advantages and Disadvantages

Answer 2

Advantage: quick way to sort data, actual data values are accessible
Disadvantages: best used only with small data sets, histogram more flexible in choice of bins

Question 3

Dot Plot

Answer 3

record data values on a number line with a dot above the number for each value observed, we can get a sense of frequency by seeing how high the dots stack up

Question 4

Dot Plot Advantages and Disadvantages

Answer 4

Advantage: Shows individual data points, helps investigate the shape of the distribution, can see points that stand out
Disadvantages: not as common as histograms and other graphs, not great for data with to many individual values

Question 5

Histograms

Answer 5

group data into interval, called bins (or classes) where the width of the interval equal the bin width, bars touch, the first value in each bin is recorded on the horizontal axis (lower class limit), the height of each rectangle corresponds to the count or proportion of the number of values in that bin

Question 6

Histogram Advantages and Disadvantages

Answer 6

Advantage: good for large data sets, helps focus on the general shape of the data
Disadvantage: individual data values are not visible, distribution shape affected by change in bin width

Question 7

Line graphs

Answer 7

use discrete (or ordinal) data in frequency table format, shows data values on x-axis, frequencies on y-axis, the frequency points are connected using line segments

Question 8

Line Graph Advantages and Disadvantages

Answer 8

Advantage: shows trends in grouped data
Disadvantage: must have data grouped by frequencies and does not work well for continuous data

Question 9

Frequency Polygons

Answer 9

continuous data must be in frequency table format, shows bins or classes on the x-axis, frequencies on the y-axis, frequency points are connected using line segments, combines idea of a histogram with line graphs

Question 10

Time series plot

Answer 10

shows the data value, or statistic, on the vertical axis with time on the horizontal axis, reveals trends, cycles or other time-oriented behavior that could not be otherwise seen in the data

Question 11

time series plot increments

Answer 11

we can look at trend over any increment of time