Transcript Mode, median and range

Mode, Median and Range
Aim:
To find the mode, median and range, and the modal
class for grouped data.
Put these numbers in numerical order with the
smallest first.
7, 3, 9, 2, 10, 8, 5, 4, 14, 12
2, 3, 4, 5, 7, 8, 9, 10, 12, 14,
34, 67, 38, 19, 44, 57, 24, 31, 62, 20
19, 20, 24, 31, 34, 38, 44, 57, 62, 67
2, -3, 1, 4, -4, 0, 5, -2
-5 -4 -3 -2 -1
-4
-3
-2
0
0
1
1
2
2
3
4
4
5
5
Averages
An average is a useful statistic because it
represents a whole set of values by just a single or
typical value.
• Where have you heard the word average
before?
• Where have you seen it used?
The Mode
 The mode is a type of average
 The mode is the value that occurs most
often in a set of data
Example
5, 6, 8, 2, 4, 5, 3, 5
MODE = 5
Sometimes there is no mode because either all the
values are different, or no single value occurs more
often than other values
THE MODE DOESN’T HAVE TO BE A
NUMBER
What letter does your first name begin
with?
What is the mode first letter for a name in
class 7Y2?
Mode, Median and Range
Aim: To find the mode, median and range,
and the modal class for grouped data.
THE MODE
PAGE 52
EXERCISE 5A
QUESTION 1
The Median
The median is another type of average
The median is the middle value for a set of
data when the values are put in numerical
order.
Example
6, 8, 3, 7, 5, 2, 4 in order
2, 3, 4, 5, 6, 7, 8
Median = 5
For an odd number of values in data set, there is only one middle value.
This is the median.
What is the median test score
for the following set of results?
5, 7, 7, 8, 10, 12, 14, 15
Median = 9
For an even number of values in a data set,
there are two middle values.
The median is the value in the middle of
these two values.
The median
PAGE 51
EXERCISE 5A
QUESTION 2
The Range
The range is not an average.
The range of a set of data is the largest
value minus the smallest value.
It shows how the data is spread out.
A small range shows that the values in a set of data are similar in size
A large range shows that the values differ considerably
Find the range:
What number month were you born in?
For example, January = 1, June = 6, and December = 12
Range = Largest number – smallest number
Range =
What does this tell us about the birthdays
of class 7Y2?
The Range
PAGE 51
EXERCISE 5A
QUESTION 3
Modal Class
For grouped data such as the example below, we cannot find the mode.
Time (Mins.)
Frequency
0-2
3-5
6-8
9-11
2
4
3
1
Modal class = 3-5
Instead, we find the MODAL CLASS. This is the group that occurs
most often.
Why isn’t it possible to calculate an exact mode or median from
grouped data?