Displaying Distributions with Graphs

•Individual:

•Variable:

Variables:

•Categorical:

•Quantitative:

•Distribution of a variable:

•Outlier:

Graphs of Quantitative Data

Dotplot

Histogram

Stemplot

Dotplot: a quick way to visualize a set of data.

Example:

Here are 18 scores from a 10 question quiz on Quadratics in Honors Math 2. Create a dot plot of the data then discuss the SOCS

100 90 90 80 70 90 40 70 60

90 80 90 90 80 100 60 80 100

Stemplot: The digit(s) in the greatest place value(s) of the data values are the stems. The digits in the next greatest are the leaves.

Example: Create a stemplot for the 25 test scores given below:

75, 8, 86, 27, 100, 83, 77, 92, 95, 66, 42, 69, 88, 100, 94, 55, 68, 72, 85, 97, 50, 91, 100, 81, 75

Split Stem: each stem is listed more than once

Example:47, 33, 33, 32, 29, 38, 23, 22, 22, 22, 21, 21, 21, 20, 20, 19, 19, 18, 18, 18, 18, 16, 15, 14, 14, 14, 12, 12, 9, 6

Back-to-Back Stemplot: allows for quick comparison

Describing or Interpreting Quantitative Data Distributions

1. Shape

2. Outliers

3. Center

4. Spread

Don’t forget your SOCS!!

Shape

• a visual description of what the distribution looks like• A distribution is ____________ if the right and left sides

of the histogram are approximately ___________ _____________.

A distribution is skewed to _________ if the right side (upper half) extends much farther out from the center than the left (lower half).

A distribution is skewed to _________ if the left side (lower half) extends much farther out from the center Than the right (upper half).

To describe the number of “humps” or “clusters” we use ________, _______, and ________.

Always skew in the _____________________________!!

Outliers

• Unusual data points far away from the bulk of the data

• Use the ________ ______________to determine if an outlier exists.

• 𝑜𝑢𝑡𝑙𝑖𝑒𝑟 < __________________

• 𝑜𝑢𝑡𝑙𝑖𝑒𝑟 >__________________________

Center

•a value that divides the observations so that about half take larger values and about half take smaller values

•Mean

•Median

Spread

•describes the variability of the data

•Range

•Variance

•Standard Deviation

•IQR

Frequency Vs Relative Frequency

Frequency:

Relative Frequency:

Use the Math II test scores below to create a frequency and relative frequency table.

100 90 90 80 70 90 40 70 60

90 80 90 90 80 100 60 80 100

Histogram:

breaks the range of values of a variable into intervals and displays only the count or percent of the observations that fall into each interval

Things to keep in mind about histograms:

1. Divide the data into _________ (intervals) of _______ width.• Need to specify classes so that each individual fall into

one class.• Usually will need between ___ and ____ intervals

2. Each bar of the histogram can include only _____ of its _________.

3. Intervals should _________ overlap.

4. _______ and ________ your axes.

5. _________ your graph!!

Classes: Data goes from ______ to _______, classes of width _______ should work.

Label and scale your axes and draw histogram.

Don’t forget the TITLE!!

Time Plot: Plots each observation against the time at which it was measures – time is always on the x-axis