Handout 9a: Box & whisker plot

How do you de-skew data?

If very skewed to right/left & want to de-skew

→ can take the square root of all values

→ can take the log of all values

What is the 5 number summary to build a box & whisker plot?

1. min value

2. Q1

3. Q2 - Median

4. Q3

5. max value

How do you build a box & whisker plot using the 5 number summary?

Median - Draw a vertical line as the median

Q1 & Q3 - Draw lines around the median to represent Q1 & Q3 and connect these lines to create a box (50% of data)

IQR - Find the IQR to be the fences (subtract IQR from median & add IQR to median to determine)

The whiskers are the biggest & smallest values that fit within the fences (25% of the data)

Any data outside of the fences are outliers! (max & min values)

What does it mean when a box & whiskers plot displays only a line?

There is only one data point for the variables

What is the 0th & 100th percentile?

• 0th percentile = minimum

• 100th percentile = maximum

• 50th percentile = Q2 (median)

What is the formula for computing percentile?

Must sort data from lowest to highest first

• Using the formula will give you the address for the percentile in question

• The 38th number in the data set gives you the 75th percentile!

What is the formula for the variance?

Variance = s²

• depends on units

What is the formula for the standard deviation?

What is the coefficient of variation?

Variation relative to the mean

• unitless