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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.