Lecture 7 Range, Quartiles and IQR - Mr. Manoo Murthy
RLeactunreg7 e, Quartiles and IQR
Range, Quartiles, and IQR
In this lesson: 1. Definition of a measure of spread
Topic on 2. Definition of range, quartiles, and interquartile range summative 3. Finding range, quartiles, and IQR with data lists
exam 4. Five ? number summaries and interpretation 5. Finding range, quartiles, and IQR with frequency tables (grouped and ungrouped tables. 6. When to use five ? number summaries and IQRs
What you should be able to do: 1. Explain the following terms: measure of spread, range, quartiles, and interquartile range. 2. Calculate the range, quartiles, interquartile range, and five ? number summaries with data lists 3. Calculate the range, quartiles, interquartile range, and five ? number summaries with ungrouped and grouped frequency tables. 4. Determine when it is appropriate to use these measures of spread in analysis.
Definition: Measure of Spread
Definition Measure of Spread
A measure of spread describes how far away from the measure of center (mean/median) entries in a data set are.
Why is it important? Consider the following scenario between the scores of 2 different classes:
Two different classes in the same grade have the following scores. A score of 50% is needed to pass, 85% is needed to get a 4. Try to decide which class has more passing students and which class has more students with a 4.
Class A:
? If we looked only at the measures of center without looking
10, 20, 30, 40, 50, 60, 70, 80, 85, 90, 100
at the data, we might think that both classes have equal
Mean = 57.72 Median = 60 7 passing students
passing students [medians are the same] but class B had
Class B:
3 students with a 4
more students with a 4 [mean of B is larger].
? The truth, however, is completely different!
55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65
? We were tricked because in class A, the data values are
Mean = 60 Median = 60 11 passing students
all far away from each other, but in class B, the data
0 students with a 4
values are all close to each other.
It is important to not just measure what number describes the middle of the data, but to also measure how spread out the data is.
Definition: Range, Quartile, and Interquartile Range
Definition Range
The spread between the largest data entry and the smallest data entry.
Range = largest number ? smallest number
Definition Quartiles
The points at which the data set is split into 4 equal parts.
Q2 = median!
50% of data
Q2
RANGE
IQR
Definition Interquartile Range [IQR]
The data range that contains the middle 50% of the entries.
IQR = Q3 ? Q1
Q1 = lower quartile
25% of data
Q1
Q3 = upper quartile
75% of data
Q3
Finding Range, Quartiles, and IQR in Data Lists
Finding quartiles is similar to finding the median!
11 numbers total
1 2 3 4 6 7 8 9 10 11 15
Range = largest number ? smallest number Range = 15 ? 1 = 14
= = .
() = = . IQR = Q3 ? Q1 = 10 - 3 =
Q1 is third observation 3 Q3 is ninth observation 10
Range = 14
Q1 = 3 Q3 = 10 IQR = 7
Step 1: Reorganize the data set in order from smallest to largest.
Step 2: To find the range, subtract the largest number from the
smallest.
Step 3:
To find Q1, divide the number of
observations by 4:
?
If
is
whole,
find
the
average of that term and
the term above.
?
If
has
a
decimal,
then
round up and choose that
number. Step 4:
To find Q3, multiply the total
number
of
observations
by
3 4
and
repeat analysis from Step 2
Step 5: To find IQR, subtract Q3 from Q1
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