Download Median and Range

Math 9 Numeracy – Unit 9.2
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Median and Range
9.2 – Median and Range
Median and Range are two measures of central tendency, or two ways in which a person
can make meaning out of data or statistics. Statistics are used by governments and
businesses to interpret information related to unemployment, inflation, industrial production
or sales numbers.
Median
The Median of a group of data is simply picking out the middle number when all of the data
is arranged in numerical order.
For example:
Mr. Trickey’s Class’s Favourite Type of Music
Category
Tally
Frequency
Rock
14
Pop
11
Punk
12
Hip Hop
10
Country
5
Alternative
6
Classical
2
If you arrange the data collected into numerical order you would get;
three on this side
2, 5 , 6 , 10 , 11, 12 , 14
three on this side
middle number
Because there is seven sets of numbers, the “10” is the middle number with three numbers
on either side of the “10”, this means that “10” is the median
If there was an EVEN number of data, you have to calculate the median. This means that
you would look at the TWO middle numbers and find the average or “mean” of the two.
two on this side
2, 5 , 6 , 10 , 11, 12
two on this side
middle numbers
Because there is six sets of numbers you have to find the average or the “mean” of both “6”
and “10”. This means you have to add both numbers and divide by the number of numbers
you added (in this case two).
Your calculations would look like this;
In this example the median would be 8.
Your turn…
Directions: Arrange the following numbers into numerical order and then identify the
median.
1.
Find the median from the following set of numbers
35, 14, 49, 26, 30, 8, 19
2. Find the median from the following set of numbers
12, 35, 24, 40, 6, 28, 16, 3
3. Find the median from the following set of numbers
122, 84, 110, 92
4. Find the median from the following set of numbers
19, 24, 17, 30, 6, 12, 18, 10, 30, 24, 19, 18, 17, 12, 10, 6
Range
The Range is the difference between the highest and lowest numbers in your data or group
of numbers. Range is an important reference point. For example if you were hired on as an
employee and your wage was set at $10 an hour, however you found out later that the range
for employees doing the same job was $9/hour to $20/hour, then you would probably want
to ask your boss what you can do to start working towards making $10/hour.
Example;
Find the range of the following numbers
28, 16, 20, 8, 32, 6, 25, 32, 28, 25, 20, 16, 8, 6
The highest number is
The lowest number is
The Range is
32
- 6
26
Your turn…
Directions: Solve the following problems as directed. SHOW ALL WORK!!!
Directions: Find the mean, median, mode and range for each group of numbers. The first
one has been done for you.
Directions: Match a definition with the correct term.
Directions: Solve for the correct answer.
Directions: Answer the following problems. Use your knowledge of Mean (average), Mode
(most frequent number), Median (middle number) or Range (difference between highest and
lowest) to answer.
1.
Sierra rode her bike around the hike and bike trail for half an hour and averaged 18
miles per hour. Ashley rode her bike around the trail and traveled 12 miles in 32
minutes. What was the difference in their average speeds? Round your answer to
the nearest tenth.
2. Mr. Trickey would receive a variety of text messages every day. If he kept a tally
chart of the number of text messages he received, then calculate the mean, median,
mode and range for one week.
Number of Test Messages Mr. Trickey Recieves in One Week
Day of the Week
Tally
Frequency
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
a.
What is the mode of text messages?
b. What is the median of text messages?
c.
What is mean (average) of text messages every day?
d. What is the range of text messages?