Measures of Shape + Examples

3 displays for measuring the shape:

3 displays for measuring the shape:

histogram, stemplot, boxplot

Histogram

1. involves having intervals each of the same size (classes)

2. counting the # of data pts that fall into each class (giving us frequency)

3. Drawing our graph w/the vertical axis being frequency & horizontal axis our variable labeled by the ends of the classes

Has 4 shapes; Right Skewed, Left Skewed, Normal/Bell, & Uniform

Right Skewed Distribution

has most of the data on the low side but few very high values on data set. So low values common & high values rare.

Found as; mean > median

Left Skewed Distribution

has most of the data on the high side but few very low values on data set. So high values common & low values rare.

Found as; mean > median

Normal/Bell Distribution

has most of the data in the middle but few very low & high values on data set

Found as; (since symmetrical) mean = median

Uniform Distribution

low values, medium values, ^ high values are all equally likely. So all values are equally likely to occur

Found as; (since symmetrical) mean = median

When using [ you need to _______ the data set to your histogram.

• Is also always on the left end

include

When using ( you need to _______ the data set to your histogram.

• Is also always on the right end

exclude

Histograms are ____ for when we have alot of quantitative data. And are only ____ because it doesn’t show the actual data points

good, bad

Stemplot

has each data pt broken into a stem & leaf portion

1. Leaves must be a single digit & are typically the last digit of each data point

2. Graph is then made by writing each distinct stem & placing all the corresponding leaves next to them

   1. can tell shape by looking at it turned on its side

   2. should ALWAYS INCLUDE a key to help the reader understand the data

Example of a Stemplot

Data set {17, 23, 36, 43, 44, 44, 48, 52, 54, 58, 58, 59 }

Key: 1 | 7

1 | 7
2 | 3
3 | 6
4 | 3, 4, 4, 8
5 | 2, 4, 8, 8, 9

Shape: Left-Skewed

Split Stemplot

where each stem is written twice

1. The first stem gets the leaves 0 through 4

2. The second stem gets leaves 5 through 9

*Should be used whenever we have 3 or less distinct stem

Interquartile Range/IQR

an outlier is a data that is far away from the general pattern of data set

• “extreme value“

• 2 ways of checking for these:

  1. Construct a Lower & Upper bound

     1. L Bound= Q1 - (1.5) x IQR

     2. R Bound= Q3 + (1.5) x IQR

  2. Any data pts lower than L bound of higher than R bound = outliers

• Is possible to have no outliers

Box plot

visual display of 5 number summary

1. Construct a horizontal axis

2. Draw a box that start at Q1 & ends at Q3. Inside the bow we draw a line @the median/M

3. Extend the lines from the box to minimum & maximum values

ONLY THE BOX is considered when determining SHAPE

Minimum & Maximum lines are called whiskers & not considered

Can only see shapes: left, right, & symmetric

What shape is this

Left Skewed Box plot

Right Skewed Box plot

Symmetric