Remember the 3 Ms?Mean, Median, and Mode

~Central Tendency~

Section 3.3

September 30, 2008

By Ms. D-H

Mean?

Mean: the sum of the data items divided by the number of data items.

These are data items:2, 3, 4, 5, 8, 8, and 12

2 + 3 + 4 + 5 + 8 + 8 + 127 (total data items)

42 / 7 = the mean, which is 6

Median?

Odd Number of Data Items: the middle number when the data items are put in numerical order.

Even Number of Data Items: the two middle numbers when data items are put in numerical order.

Median is the middle of the road

Median?

So find the median with these data items. 2, 3, 4, 5, 8, 8, and 12 They’re in order There are 7 numbers, meaning odd. So which is the middle most number? The median is 5.

Mode?

Mode: is the data item that occurs most often.

There can be one mode, multiple modes, or no mode. You can say how many modes there are too!

What about our previous data set? 2, 3, 4, 5, 8, 8, and 12 8 is a mode for these data items.

Find me the M, M & Ms

12, 14, 26, 37, 8, and 14 Re-order: 8, 12, 14, 14, 26, 37. Mean: 18.5 Median: 14 How many Modes: 1 Mode: 14

Find me the M, M & Ms

2.3, 4.3, 3.2, 2.9, 2.7, and 2.3. Re-order: 2.3, 2.3, 2.7, 2.9, 3.2, 4.3. Mean: 2.95 Median: 2.8 How many Modes? 1 Mode: 2.3

Find me ONLY Mode:

Grape, grape, banana, nectarine, strawberry, strawberry, strawberry, orange, watermelon.

How many modes? Just one: strawberry.

How many modes?

11, 9, 7, 7, 8, 8, 13, 11 3 Modes 38.5, 55.4, 45.3, 38.5, 68.4 1 Mode

Outlier

Outlier: is a data item (data value) that is much higher or lower than the other data values.

Outliers can affect the mean of a group of data.

Example: 2, 3.5, 1, 2.5, 5 billion. Example: 35, 45, 40, 37, -6.

Describing Data with M, M, & M.

You can use what you know about Mean, Median, and Mode to describe data.

But figuring out which M describes it best is difficult.

I think mode describes it best!

Nah! Its got to be mean!

Which M, M, & M is best?

The favorite movie of students in the eighth grade class?

Mode: good for non-numerical data items and for frequent occurrences.

Which M, M, & M is best?

The distances students in your class travel to school.

Median: one student may live much further than everyone else. When an outlier may significantly influence the mean, we use median.

Which M, M, & M is best?

The daily high temperature during a week in July.

Mean: since daily temp. are not likely to have outlier, mean is best. When data have no outlier, use mean.

Measures and Central Tendency

Your text book is going to ask you determine which MEASURE of CENTRAL TENDENCY best describe the data.

Its just asking you to figure out which M works with the data best!

Using FormulasSection 3.4

Just two formulas.

Substituting into Formulas

Formula is an equation that shows a relationship between quantities that are represented by variables.

Like: Susie has b books. b is the number of books Susie has. b stands for something.

Rate

Distance = rate • (time) d = rt Cause remember? r and t next to each

other means you multiply them. So…rate multiplied by time = distance.

Obvious Example: d = r • t

Suppose Ms. Dewey-Hoffman traveled 162 miles in 2 hours. Use the formula.

How fast was I going? What was my rate? d = r • t d = distance, or 162 miles. t = time, or 2 hours. 162 miles = r • 2 hours.

Obvious Example: d = r • t

Suppose Ms. Dewey-Hoffman traveled 162 miles in 2 hours. Use the formula.

What was my rate? 162 miles = r • 2 hours.

2 hours 2 hours 162 2 = 82 miles/hour So, Ms. Dewey-Hoffman was traveling at 82 miles/hour

to go 162 miles in 2 hours. 82 mph is my r or rate. =]

Try These: d = r • t

d = 200 yards, t = 24 seconds What don’t we know? Set up equation.

Solve. r = 30 feet/minute, t = 5 minutes What don’t we know? Set up equation.

Solve.

Perimeter Formula: P = 2l + 2w.

Perimeter = 2(length) + 2(width).

W W

L

L • The formula simplifies how the perimeter of a rectangle works.

• Perimeter = l + l + w + w…so…

• Perimeter = 2l + 2w

Try These: Tell Me Perimeter

Remember: P = 2l + 2w

Length = 16.8cm, Width = 27.3cm

Length = 8.6cm, Width = 17.4cm

W

L

Assignment #16

Pages: 134-135: # 5-8 All, 15-18 All. Pages: 139-140: # 5–21 Odd. Make sure you answer ALL parts of each

problem, the first set of problems ask for a lot.