The
interquartile
range, the
range and the
mode
SUMMARY STATISTICS
 After
displaying data using a histogram or
stem plot, we can make even more sense
of the data by calculating what are
called summary statistics. They give us an
idea about:
1. Where the centre of the distribution is
2. How the distribution is spread out.
5 Summary Statistics
 Median
 Interquartile
range
 Range
 Mode
 Median
(this will be looked at later)
The Median
The median is the midpoint of a set of data.
 Half the data are less than or equal to the
median
 We can use the rule :
where ‘n’ is
the no. of observations. This will tell us the
POSITION of the median.
 Eg: 2, 5, 6, 8, 11, 12, 15
-How many observations?
-Is it in order???

Ans: median = 7 + 8 /2 = 7.5
TESTING YOUR KNOWLEDGE
The Interquartile Range
 This
divides a set of data into quarters. This
is referred to as “Quartiles”.
 The symbols used to refer to these
quartiles are Q1, Q2, Q3.
 Q2= median
 The interquartile range IQR= Q3 – Q1
 The IQR gives us the range of the middle
50% of values in a set of data.
IQR = Q3- Q1
•
•
•
•
Step 1: Write down the data in ordered form
from lowest to highest
Step 2: Locate the median; that is, locate Q2.
Step 3: Now consider just the lower half of the
set of data. Find the middle score. This score is
Q1.
Step 4: Now consider just the upper half of the
set of data. Find the middle score. This score is
Q3. The four cases given in the next slide
illustrate this method.
TESTING YOUR KNOWLEDGE
The range
 The
range of a set of data is the
difference between the highest and
lowest values in that set.
 You can use the calc: minX and maxX
 Range= maximum-minimum
The mode
 Most
occurring/often score.
 If there is more than one score with the
highest frequency, then all scores with
that frequency are the modes.
 The mode is a weak measure of the
center of data because it may be a value
that is close to the extremes of the data.
 Look at the previous slide!
Classwork/Homework
 Ex
1E pg 22 Q’s 1-8