Chapter 1: Exploring Data

Lesson 4: Quartiles, Percentiles, and Box Plots

Mrs. Parziale

Vocabulary:• Quartiles: divide the data

into _________ roughly even parts.

• To find Quartiles: – Line up scores numerically – locate

the median.– That divides the data in half, thus

marking the division between the 2nd and 3rd quartiles.

– First quartile Q1 is the median of the lower half of data.

– Third quartile Q3 is the median of the higher half of data.

four

More Vocabulary

• five number summary: Min, Q1, Median, Q3, Max

• box-and-whiskers plot: a visual representation of the 5-num sum

• interquartile range: (Q3 – Q1) ; the ___________ of the middle 50% of the data. This measures the _____________________ of data around the median

range

concentration

Example 1:

Use the College Costs data to the right. Find the data needed to make a box plot.

• find the median value.• Find Q1• Find Q3• What is the 5-num summary?• Find the interquartile range (IQR)

How to make a box plot:Five Number Summary is: 4205, 5324, 6169, 7922, 10401 1. Draw a number line including minimum and max values2. Draw a rectangle with vertical opposite sides at Q1 and Q3. (the

hinges)3. Draw a line parallel to the hinges at the median.4. Draw segments from the midpoint of the hinges to the min and max

(the whiskers)

Yet More Vocab

percentile: the pth percentile of a set of numbers is a ______________________ such that p percent of the numbers are ______________________ to that value. – all points in data set are less than or equal to the max

(100th percentile)– median is the __________ percentile– Q1 is the ___________ percentile

– Q3 is the __________ percentile

value in the set

75th 25th

50th

less than or equal

Example 1, cont.• What percentile is the first value of our data

(Oklahoma)? =

• g) What percentile rank is New Jersey? =

• h) What is the cost of the college at the 66th percentile?

.66 = =

index

total

48

50

50

index

Using Your TI83

• Using the following dataset: {1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 6, 6, 24}

• Enter data into calculator using STAT EDIT• Press 2nd STATPLOT • Press GRAPH• Choose box plots• Use TRACE to find the values of the 5-num

summary.

Steps to take when you want to know if something is an outlier?

Using the following data (same as previous slide), find the outlier. {1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 6, 6, 24}

1. Find Q3 – Q1 (the IQR)

2. Take 1.5*IQR and add it to the Q3

3. Take 1.5*IQR and subtract it from the Q1.

4. Anything above or below that number is an outlier.

{1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 5, 6, 6, 24}

Closure

• Use your calculator to create a box plot for the following data.

{1, 4, 5, 5, 5, 6, 6, 7, 8, 12, 23}

• Find any outliers.