UNIT 8 Section 4 Distributed Practice #1. MEAN * Mean is the average of a set of numbers. To find...

UNIT 8

Section 4 Distributed Practice Section 4 Distributed Practice #1#1

MEANMEAN ** Mean Mean is the average of a is the average of a

set of numbers.set of numbers.

To find the mean, or To find the mean, or average of a set of data, average of a set of data, add the numbers and divide add the numbers and divide by the number of entrees.by the number of entrees.

Example 1Example 1: Find the : Find the mean of this set of mean of this set of

data:data: 1, 2, 3, 2, 5, 7, 3, 4, 2, 11, 2, 3, 2, 5, 7, 3, 4, 2, 1

Sum:Sum: 1 + 2 + 3 + 2 + 5 + 7 + 3 + 4 + 2 + 1 = 301 + 2 + 3 + 2 + 5 + 7 + 3 + 4 + 2 + 1 = 30

30 / 10 = 330 / 10 = 3

THE MEAN OF THIS SET THE MEAN OF THIS SET OF DATA IS 3!!OF DATA IS 3!!

MEDIANMEDIAN * The * The median median is the middle is the middle

number when a set of data number when a set of data is arranged from smallest to is arranged from smallest to largest.largest. In the case of In the case of two middle two middle

numbersnumbers, find the average , find the average of the two to determine the of the two to determine the

median.median.

Example 2:Example 2: Find Find the median of the the median of the

set of data:set of data: 8, 5, 4, 9, 11, 2, 148, 5, 4, 9, 11, 2, 14

Put in order: Put in order:

2, 4, 5, 8, 9, 11, 142, 4, 5, 8, 9, 11, 14

The median of the set of The median of the set of data is 8!!data is 8!!

Example 3: Example 3: Find the Find the median of the set of median of the set of

data:data: 23, 14, 25, 32, 17, 4023, 14, 25, 32, 17, 40

Put them in order:Put them in order:

14, 17, 23, 25, 32, 4014, 17, 23, 25, 32, 40Average the two: 23 + 25= 48Average the two: 23 + 25= 48

48/2 = 2448/2 = 24The median of the set of The median of the set of

data is 24!!data is 24!!

MODEMODE * The * The modemode of a set of data is of a set of data is

the number that occurs most the number that occurs most frequently.frequently.

Example 5: Example 5: Find Find the mode of the set the mode of the set

of data:of data: 8, 3, 2, 9, 10, 5, 11, 3, 2, 5, 10, 28, 3, 2, 9, 10, 5, 11, 3, 2, 5, 10, 2

The mode of the The mode of the set of data is 2!!set of data is 2!!

Some sets of data Some sets of data have have no modeno mode and and some sets of data have some sets of data have more than onemore than one mode. mode.

MODEMODE

Box and Whisker Plot

A box and whisker plot is a method of representing data.It looks like this:

BOXES


A box and whisker plot is a method of representing data.It looks like this:

WhiskersWhiskers


In a box and whisker plot, the boxes represent 50% of the data while each whisker represents 25% of the data. The total represented by the entire plot is 100%

25%25% 50%

Drawing a Box and Whisker Plot

To draw a box and whisker plot, you must first find 5 things:

1.1. Least Value – Lower ExtremeLeast Value – Lower Extreme2.2. Greatest Value – Upper ExtremeGreatest Value – Upper Extreme

3.3. Quartile 1 –Lower QuartileQuartile 1 –Lower Quartile4.4. Quartile 2Quartile 2

5.5. Quartile 3Quartile 3 - upper quartile upper quartile

(median of 1st half)

(median)

(median of 2nd half)

Example 1

Draw a box and whisker plot for this data:

4, 7, 15, 27, 9, 14, 12, 22, 9, 11, 184, 7, 15, 27, 9, 14, 12, 22, 9, 11, 18

First, we must put these numbers in order from least to greatest.

Example 1


4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 274, 7, 9, 9, 11, 12, 14, 15, 18, 22, 27

Now we can find those 5 things that we need.

Example 1


4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 274, 7, 9, 9, 11, 12, 14, 15, 18, 22, 271.1. Least ValueLeast Value

2.2. Greatest ValueGreatest Value

3.3. Quartile 1Quartile 1



Example 1


4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 274, 7, 9, 9, 11, 12, 14, 15, 18, 22, 271.1. Least Value --- Least Value --- 44

2.2. Greatest Value --- Greatest Value --- 2727




Quartile 2LetLet’’s find Quartile 2 first. s find Quartile 2 first. It is the median of the entire group of data.It is the median of the entire group of data.What number is in the middle?What number is in the middle?

4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 274, 7, 9, 9, 11, 12, 14, 15, 18, 22, 27

Example 1





4.4. Quartile 2 --- Quartile 2 --- 1212


Quartile 1LetLet’’s find Quartile 1 next. s find Quartile 1 next. It is the median of the 1It is the median of the 1stst half of data. half of data.What number is in the middle?What number is in the middle?

4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 274, 7, 9, 9, 11, 12, 14, 15, 18, 22, 27

1st half

Example 1







Quartile 1LetLet’’s find Quartile 3 next. s find Quartile 3 next. It is the median of the 2It is the median of the 2ndnd half of data. half of data.What number is in the middle?What number is in the middle?

4, 7, 9, 9, 11, 12, 14, 15, 18, 22, 274, 7, 9, 9, 11, 12, 14, 15, 18, 22, 27

2nd half

Example 1







Now we can draw a box and whisker plot for this data.

Draw a number line that is large enough to include the smallest and largest number.

Example 1

3030282826262424222220201818161614141212101088664422

Example 1Place a dot on the smallest number and

largest number.

3030282826262424222220201818161614141212101088664422

Example 1Draw a vertical line on each quartile.

3030282826262424222220201818161614141212101088664422

Example 1Draw horizontal lines to make the boxes.

3030282826262424222220201818161614141212101088664422

Example 1Connect the least and greatest value to

create the whiskers.

3030282826262424222220201818161614141212101088664422

Example 1

3030282826262424222220201818161614141212101088664422

Stem and Leaf

A stem-and-leaf plot is a table that represents a group of numbers. (data) The leaves represents numbers in the ones place. The stems represents numbers in the tens and hundreds places.

Drawing a Stem and Leaf Plot

Draw an ordered stem-and-leaf plot Draw an ordered stem-and-leaf plot for the following data for the price of for the following data for the price of tennis shoes. Make sure the graph is tennis shoes. Make sure the graph is properly labeled.properly labeled.


PRICES OF TENNIS SHOES:PRICES OF TENNIS SHOES:

82, 69, 25, 55, 75, 88, 99, 64, 82, 125, 7082, 69, 25, 55, 75, 88, 99, 64, 82, 125, 70

Drawing a Stem and Leaf PlotPRICES OF TENNIS SHOES:PRICES OF TENNIS SHOES:

82, 69, 25, 55, 75, 88, 99, 64, 82, 125, 7082, 69, 25, 55, 75, 88, 99, 64, 82, 125, 70Our first step is to write the numbers in

order from least to greatest.


Our next step is to draw a table with two columns -- one for stems and one for leaves

PRICES OF TENNIS SHOES:PRICES OF TENNIS SHOES:

25, 55, 64, 69, 70, 75, 82, 82, 88, 99, 12525, 55, 64, 69, 70, 75, 82, 82, 88, 99, 125


25, 55, 64, 69, 70, 75, 82, 82, 88, 99, 12525, 55, 64, 69, 70, 75, 82, 82, 88, 99, 125StemsStems LeavesLeavesOur next step is to fill in the

table.

Remember the stem represents the numbers in the tens and

hundreds places and the leaves represent the numbers in the

ones place


25, 55, 64, 69, 70, 75, 82, 82, 88, 99, 12525, 55, 64, 69, 70, 75, 82, 82, 88, 99, 125StemsStems LeavesLeaves22 55


25, 55, 64, 69, 70, 75, 82, 82, 88, 99, 12525, 55, 64, 69, 70, 75, 82, 82, 88, 99, 125StemsStems LeavesLeaves22 5555 55


25, 55, 64, 69, 70, 75, 82, 82, 88, 99, 12525, 55, 64, 69, 70, 75, 82, 82, 88, 99, 125StemsStems LeavesLeaves22 5555 5566 4 94 9


25, 55, 64, 69, 70, 75, 82, 82, 88, 99, 12525, 55, 64, 69, 70, 75, 82, 82, 88, 99, 125StemsStems LeavesLeaves22 5555 5566 4 94 977 0 50 5


25, 55, 64, 69, 70, 75, 82, 82, 88, 99, 12525, 55, 64, 69, 70, 75, 82, 82, 88, 99, 125StemsStems LeavesLeaves22 5555 5566 4 94 977 0 50 588 2 2 82 2 8


25, 55, 64, 69, 70, 75, 82, 82, 88, 99, 12525, 55, 64, 69, 70, 75, 82, 82, 88, 99, 125StemsStems LeavesLeaves22 5555 5566 4 94 977 0 50 588 2 2 82 2 899 99


25, 55, 64, 69, 70, 75, 82, 82, 88, 99, 12525, 55, 64, 69, 70, 75, 82, 82, 88, 99, 125StemsStems LeavesLeaves22 5555 5566 4 94 977 0 50 588 2 2 82 2 899 991212 55

WAIT! !

There’s a problem with our stem and leaf plot. In a stem and leaf plot, you don’t skip numbers in the stems. If there is no leaf for a stem, then you leave it blank.Let’s go back to the last example.

PRICES OF TENNIS SHOES:PRICES OF TENNIS SHOES:StemsStems LeavesLeaves22 553344 55 5566 4 94 977 0 50 588 2 2 82 2 899 99101011111212 55

This is the correct way to draw the stem and leaf plot for our data.

UNIT 8 Section 4 Distributed Practice #1. MEAN * Mean is the average of a set of numbers. To find...

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