Download To Create a Box Plot - Mrs. Kleimeyer

Describing Data Numerically
• Measures of Center –
mean, median
• Measures of Spread –
range, interquartile
range, standard
deviation
S-ID.2 Use statistics appropriate to
the shape of the data distribution
to compare center (median, mean)
and spread (interquartile range,
standard deviation) of two or more
different data sets.
To Create a Box Plot
•Order the numbers from least to
greatest and find the median.
• The median breaks the numbers into
two groups. The Lower & Upper
Quartiles.
•Find median of the lower quartile.
•The median of the lower quartile is Q1.
•Find the median of the upper quartile.
•The median of the upper quartile is Q3.
•Find the minimum and maximum
-Plot the median, Q1, Q3, maximum and the minimum on a number
line with a dot.
This the 5 number summary.
-Make a rectangle going from Q1 to Q3 and passing through median.
-Make a vertical line at the median, going through your rectangle.
-Extend a single line from the rectangle to the minimum
-Extend a single line from the rectangle to the maximum.
Practice!
•1,9,3,6,9,8,3,5,7,2,5,2,4
Write these examples!
• Ex: 3,4,5,6,7-->median=5--> exclude 5 to find Q1 and Q3.
• Ex: 3,4,5,6,7,8--->median=5.5--->use 5 and 6 for Q1 & Q3
• Ex: 3,4,5,5,6,7--> median is 5, but a tie between 5 & 5 so
use the first 5 for Q1 & 2nd 5 for Q3
•The Interquartile Range is the spread
of the middle 50% of the data.
•It is shown by the length of the box.
•Found by subtracting Q3-Q1
Finding Outliers
1.5IQR rule
1. Calculate the IQR.
2. Multiply the IQR by 1.5.
3. Add this number to Q3. Any value above this
amount is considered an outlier.
4. Subtract that number from Q1. Any value below
this amount is an outlier.
**Why 1.5? John Tukey, the statistician who devised this rule, is quoted as saying that
“one was not enough and two was too many. “
•1,9,3,6,9,8,3,5,7,2,5,2,4
•1,2,2,3,3,4,5,5,6,7,8,9,9
•Min: 1 Q1: 2.5 Med: 5
Q3: 7.5 Max: 9
•Use 1.5IQR rule to find # outliers below
______= IQR 1.5 (______)=
7.5+______=____________
•Use rule to find # outliers above
2.5-_______=_________
Interpreting Measures of Spread
• Range: max – min; spread of the entire data set –
sensitive to outliers
• IQR: Q3 – Q1; spread of the middle 50% of the data –
not sensitive to outliers
• Standard Deviation: the typical amount that a data
value varies from the mean – sensitive to
outliers
How do you decide whether
to use the mean and
standard deviation or the
median and IQR to
summarize the data
numerically?
Outliers
35, 37, 39, 39, 37, 20, 29, 25
• Create a box plot of the data. Scale: 5, mark the number line by 5’s
• What is the 5-number summary? Min, Q1, Med, Q3, Max
• What do you multiply the IQR by to find outliers?
• What would a number have to be less than to be an outlier to this
data set?
• What would a number have to be greater than to be an outlier of this
data set?
• List any outliers
90,70,75,80,81,89,65
• Create a box plot of the data. Interval: 5, mark the number line by 5’s
• What is the 5-number summary? Min, Q1, Med, Q3, Max
• Outliers?