Math 9 Numeracy– Unit 9.2

-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;

2, 5, 6, 10 , 11, 12, 14

three on this sidethree 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.

2, 5, 6,10 , 11, 12

two on this sidetwo 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

  1. Find the median from the following set of numbers

12, 35, 24, 40, 6, 28, 16, 3

  1. Find the median from the following set of numbers

122, 84, 110, 92

  1. 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 32

The lowest number is- 6

The Range is 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.
  1. 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 /
  1. What is the mode of text messages?
  1. What is the median of text messages?
  1. What is mean (average) of text messages every day?
  1. What is the range of text messages?