Statistics & Graphs

Unit 1 Home

61 Mean, Medians, Modes and Ranges60 Central Tendency, Find Data59 Frequency distributions and line plots58 Bar Graphs57 Scatter plots56 Histograms55 Circle graphs54 Stem-and-leaf plots53 Misleading graphs

Statistics & Graphs

Quote

A man who is not somewhat of a poet can

never be a mathematician.

Karl Weierstrass (VEER strass)

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Puzzle – Are you really awake?

A certain five letter word becomes shorter when you add

two letters to it. What is the word?

SHORT

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61 a Means, Medians, Modes and Ranges

Mean = Average of the data. -Add them up and divide by the number of items you have

Median = Middle value of data

-Arrange data in order, choose the middle value

-If there is no middle number, the Median is the average of the middle numbers

Mode = Value that occurs the most

-Data with no repeats has no mode

-Several repeats occurring same number of times has several modes

Range = High value minus the low value

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61b Means, Medians, Modes and Ranges

What is the Mean, Median, Mode and Range for the data?

8, 7, 20, 8, 22, 7, 7, 9, 4, 28

Mean =

10

284977228207812

Median = 4, 7, 7, 7, 8, 8, 9, 20, 22, 28

Since there are two middle numbers take the average of the two middle numbers which is 8, The median is 8

Mode = 7 Range = 28-4 = 24

12, 8, 7, 24

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61c Means, Medians, Modes and Ranges

For the first three sets of numbers below, the value of x represents the same type of measurement for central tendency. Find the value of x for the fourth set of numbers

515202550

x=20

48

16284052

x=22

1622222224

x=22

131317232929

x =___ 20

What type of measurement does x represent?___________Median

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61d Activity

1) Form a group of four or five people of the same gender

2) Measure each persons height and total arm length in cm-Record this information alongside their name

4) Calculate mean, median, mode & range for the class. (M & F)Do this for height and arm length separately for M & F.

Have in your notebook the height and arm length of everyone in this class….. You will need this data later…!

3) Place your name, height, and arm length on the board-copy this information into your notebook

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60 Quote

The pursuit of an idea is as exciting as the pursuit

of a whale.

Henri Poincare (pain ca RAY)

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60 Puzzle – Anyone want some coffee?

If boiling water is poured into a thick drinking glass or into a very thin wine

glass, of the two, which is more likely to crack?

The thick glass is more likely to

crack.

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60a Central Tendency – Find data

(ex2) Martha averaged 21 points per game last season and was the leading scorer on her basketball team. This year she has already scored 102 points in 5 games. Which equation can be used to find P, the number of points she must score in the 6th game to tie her last year’s average?

(ex1) Catherine scored 152 and 165 for her first two bowling games. What score will she have to achieve on her third game to have an average of 170?

1703

165152

x

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60b Central Tendency – Find data

(ex3) A group of four items have a mean of 63.

What would the value of the fifth item have to be in order to produce a mean of 57?

(ex4) You are shipping items for a shipping company. The items weigh 32, 34, 23, 35, 45 pounds each. You are going to add one more item weighing 52 pounds. Which would increase more by adding the last package, then mean or the median?

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59Quote

Let no one ignorant of geometry enter here.

Plato (PLAY toe)

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59 Puzzle – How many words are there?

There is a word in the English language that the first two letters signify a male, the first three letters signify a female, the first

four signify a great male and the whole word signify a great female.

What is the word?

Heroin

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59a – Frequency distributions and line plots

Frequency distribution = a display of how FREQUENTLY something occurred.

Line plots = a graphical display using a number line to showdata.

Ex1. The pulse rates of students before physical education class are recorded in the table.

Pulse Rate 68 69 70 71 72 73 74 75 76 77

Number of Students 3 4 0 0 5 2 1 4 3 1

How many students had a pulse rate lower than 74? _______14

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59b – Frequency distributions and line plots

Ex2. The line plot below shows the number of books read in a year by Swain Elementary School students. Each X represents 5 students. How many students read 10 or fewer books?

50 students read 10 or fewer books

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59c – Frequency distributions and line plots

Ex3. The numbers below represent the ages of the playerson a softball team. Make a line plot to show the data.

29, 26, 25, 32, 27, 25, 32, 26, 24, 25

What numbers do we need on the number line? _______24-32

23 24 25 26 27 28 29 30 31 32 33x

xxx

xx x x

xx

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59d – Activity

Construct a line plot using the height of the people in your class.

Be sure you are using the height and make it look orderly. This is to be turned in for grading.

On you paper, include your names, date and class period

Don’t forget to label your graph so we know what it means.

Use a different color for plots of the Boys and Girls

Do this again for the Arm Span measurements.

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Quote

There are two dangerous extremes.

One is to shut reason out, the other is to let nothing in.

Blaise Pascal (pass CAL)

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58 Puzzle – Fish anyone?

Two mothers and two daughters were fishing. They managed to

catch one 5 pound fish, one 3 pound fish, and one 2 pound fish.

How is it that they were each able to take home a fish?

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58a - Bar Graphs

Bar Graph = A graphical display representing data in different categories or groups. The length of a rectangle or bar is used to represent the numerical amount.

Labels

Statistics & Graphs

58b - Bar Graphs

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58c - Bar Graphs

The graph below shows the sales of various vehicles by one dealer for the month of April. Approximately what percent fewer coupes were sold than sedans?

xcoupes

sedans 100

x

100

900

1200

Cross Multiply 1200x =90000

Divide by 12 x=75

25% fewer coupes were sold than sedans

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58d - Bar Graphs

The graph below shows the sales of various vehicles by one dealer for the month of April. Approximately how many times more compacts were sold than sedans?

xcompacts

sedans 1

x

1

18

12

Cross multiply 12x=18

Divide by 12 x=1.5

About 1.5 times more compacts were sold than sedans

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Quote

If I have seen further than [others], it is by

standing upon the shoulders of Giants.

Isaac Newton

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57 Puzzle – Need some stamps

How many three cent stamps are in a dozen?

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57a Scatter Plots

Scatter Plot = Graph showing dots for points of data

Line of best fit = Approximate line showing relations of graph

Strong + Relation

Strong- Relation

Moderate+ relation

No correlation

A Weak Relationship implies a spread out points

A Strong relationship implies close to line

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57b Scatter Plots

The table shows the relationship between the time a student spends typing each week and his percent improvement on speed assessments.

On graph paper, make a scatter plot of percent improvement vs. practice hours and then draw the line of best fit. Using the line of best fit, estimate what percent gain would be expected if the number of practice hours is 4 hours.

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57c Scatter Plots

% I

mpr

ovem

ent

60

50

40

30

20

10

2 4 6 8 10 12 14 16 18 20

Practice Time Vs. Improvement

Practice Hours4 hours? Approx 12% imp

Statistics & Graphs

57 Activity

Construct a scatter plot for height VS. Arm length

Draw a “line of best fit”

Label your graph.

Do you feel there is a connection between height and arm length? Why?

Arm length (cm)

Student height (cm)

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Quote

There is no branch of mathematics which may not be applied to the real

world.Nicolai Lobachevsky

(L0 ba CHEFF ski)

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56 Puzzle - Ships

There are two ships of equal size and strength. One is made of wood

and one is made of steel.

Can you explain which is heavier?

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56a Histograms

Histogram = histogram is a graphical display of frequencies. A histogram shows what proportion of cases fall into each of several or many specified categories.

The categories are usually specified as non-overlapping intervals of some variable. The categories (bars) must be adjacent

Relative frequency=

The frequency that something occurred divided by how many samples were taken.

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56b Histograms

The golf scores for the basketball team are listed below. Make a histogram using ten-point intervals to show the distribution of scores.

88, 105, 71, 84, 107, 99, 115, 78, 86, 93, 102, 74, 119, 98, 102, 86, 81, 95, 83, 97, 95, 99, 94, 96, 92

Score Fre. R.F.

70-79

80-89

90-99

100-109

110-119 70 80 90 100 110 120 Golf Scores

Frequency 2

468

1012

Current Golf Scores

3

6

10

4

2

.12

.24

.4

.16

.08

Statistics & Graphs

56c Histograms

Use the histogram below to find the total frequency for the interval from 1.5 to 3.5.

The frequency from 1.5 to 3.5 is 35 times

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56d Activity

Construct a graph (Histogram) showing the heights of students from activity 65 (Total Class)

Construct a graph (Histogram) showing the Total arm length of students from activity 65 (Total Class)

Number of students

Height / Length

654321

121-135 136-140 141-145 146-150

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Quote

It is unworthy of excellent men to lose hours like slaves in the labor of

calculation which could safely be relegated to anyone else if machines

were used.

Gottfried Wilhelm Leibniz (LIPEnitz)

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55 Puzzle – Can you say this correctly?

What word in the English language does every Harvard graduate

pronounce wrong?

Clue: You pronounce it wrong as well!

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55a Circle graphs

Circle graph Pie graph (3- dimensional)

How many degrees are in a circle? _____360°

A full circle represents what percent? _____100%

To work with circle graphs, use proportions to solve for additional information.

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55b Circle graphs

The circle graph below represents a family’s monthly budget. If the total monthly income is $2100, how much money is spent on food?

Circle

100

25

Income

2100

x

Cross multiply 100x = 52500

Divide by 100 x=525

$525 are spent on food.

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55c Circle graphs

Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The results are shown in the circle graph below. About how much time altogether was spent on homework and sleeping?

100

41

24

x

100x=984

x=9.84 hours

or about 10 hours

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55d Circle graphs

The circle graph below represents a student’s spending. Estimate the fraction of the budget that was spent on food.

MusicOther

Food

5

1)A

5

3)B

20

3)C

3

1)D

Convert each fraction to a % (Divide)

.2 .6 .15 .33

Your answer should be just less that ¼.

Which answer should we choose?

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55e Circle graphs

A survey about a music program found that 300 students wanted after-school music programs, 180 students wanted music programs during the day, and 120 students did not want a music program at all.

If a circle graph were made using this data, what would the measure of the central angle be for the “in-school” group?

600

180

600 is the total of the students

360

x 600x=64800

x=108

The angle is 108°

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Quote

The theory of probability is at bottom only common sense.

Pierre Simon de Laplace

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54 Puzzle – Got $$$

If nine thousand, nine hundred, nine dollars is written as:

$9,909

How should twelve thousand, twelve hundred, twelve dollars be written?

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54a Stem-and-leaf plots

Original data set

22, 25, 25, 31, 31, 31, 32, 35,40, 40, 43, 44, 46, 47, 53, 53,

55, 58, 59, 59, 62, 62, 63

Find the mean, median, mode and the range.

Mean 44.17

Median = 44

Mode = 31

Range = 41

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54b Stem-and-leaf plots

What data is represented by the stem-and-leaf plot below?

9101112

3 6 8

0 3 61 3 9

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Quote

The most important questions of life are . . .

really only problems of probability.

Pierre Simon de Laplace