Analyzing and Interpreting Data To understand a set of data, you need to organize and summarize the values. A measure of central tendency is used to.

Analyzing Analyzing and and

Interpreting Interpreting DataData

To understand a set of data, you need to organize and summarize the values.

A measure of central tendency is used to describe a typical value in the

data set.

The Mean, median, and mode are all

measures of central tendency.

MEANMEAN

TheThe Mean Mean is the is the numerical numerical averageaverage of a data set. of a data set.

MeanMean = = sum of the data itemssum of the data itemstotal number of data itemstotal number of data items

MEANMEAN Determine the Determine the meanmean of this data set: of this data set: 2, 5, 8, 13, 19, 24, 28, 372, 5, 8, 13, 19, 24, 28, 37

Find the sum of the data values.Find the sum of the data values.2+5+8+13+19+24+28+37 =2+5+8+13+19+24+28+37 =

How many items are in this data set?How many items are in this data set? Calculate the Calculate the meanmean..

136 / 8136 / 8 = =

136136

88

1717

MEDIANMEDIANThe The medianmedian is the is the middle valuemiddle value in in the data set when the numbers are the data set when the numbers are arranged in order from least to greatest.arranged in order from least to greatest.

2 6 8 11 152 6 8 11 15

MEDIANMEDIAN

For a set containing an even number of For a set containing an even number of data items, the data items, the medianmedian is the is the numericalnumerical average of the two average of the two middle data valuesmiddle data values. .

4 7 8 9 16 184 7 8 9 16 18

The mean of 8 and 9 is 8.5, so 8.5 is the MEDIAN.

MODEMODE

The The modemode is the data item that occurs is the data item that occurs the the mostmost often. often.

There can be more than one mode:There can be more than one mode:

Ex. 5 6 8 10 5 10 7 Ex. 5 6 8 10 5 10 7

Mode:Mode: 5 and 10 5 and 10

MODEMODE

Determine the Determine the modemode of this data of this data set.set.

2, 5, 8, 13, 19, 24, 28, 37, 2, 5, 8, 13, 19, 24, 28, 37,

25, 18, 2, 35, 3, 5, 19, 13, 525, 18, 2, 35, 3, 5, 19, 13, 5

Find values that are the same.Find values that are the same.

The The modemode is . is . 55

We can use the calculator We can use the calculator STATSTAT key to locate the MEAN key to locate the MEAN

and the MEDIAN:and the MEDIAN: Data: 4 6 7 12 6Data: 4 6 7 12 6

Step 1: Enter the data into list 1 in your Step 1: Enter the data into list 1 in your calculator (calculator (STAT EDITSTAT EDIT).).

Step 2: “Tell” your calculator to determine Step 2: “Tell” your calculator to determine the measures of central tendency. (the measures of central tendency. (STAT STAT CALCCALC, , ENTERENTER on 1) on 1)

Read the answers!Read the answers!

x mean = 7

Scroll down to MED to locate the Scroll down to MED to locate the median value:median value:

MED = 6MED = 6

Note: The calculator cannot “tell” Note: The calculator cannot “tell” you the mode. you the mode.

So… determine what value is the So… determine what value is the most frequent in your data:most frequent in your data:

4 6 7 12 64 6 7 12 6 The MODE = 6The MODE = 6

OUTLIERSOUTLIERS

An An outlieroutlier is a data value that is a data value that is much higher or lower than is much higher or lower than the other data values in the set. the other data values in the set.

(think: (think: outlawoutlaw someone whose someone whose

activities activities lie lie outoutside side the law)the law)

What is the What is the OUTLIEROUTLIER in this data in this data set?set?3, 5, 1, 8, 6, 10, 2, 9, 5, 65, 4, 7, 5, 33, 5, 1, 8, 6, 10, 2, 9, 5, 65, 4, 7, 5, 3

Let’s go back to our earlier Let’s go back to our earlier data:data:

4 6 7 17 64 6 7 17 6

Mean = 8Mean = 8 Median = 6Median = 6 Mode = 6Mode = 6

Does the MEAN or the MEDIAN represent Does the MEAN or the MEDIAN represent the “typical” value in the data? Why?the “typical” value in the data? Why?

RANGE of a Data SetRANGE of a Data Set

The The RANGERANGE is the difference between is the difference between the highest (the highest (maximummaximum) and lowest ) and lowest ((minimumminimum) value.) value.

Given: 4 7 9 10 3Given: 4 7 9 10 3 What is the range? What is the range?

Answer: 10-3= Answer: 10-3= 77

Question 1:Question 1: A computer company had a A computer company had a

warehouse sale. The sales manager warehouse sale. The sales manager found that the mode of the sale found that the mode of the sale prices of computers was $1,200. prices of computers was $1,200. What does this price represent?What does this price represent?

Half of the computers sold for $1,200. Half of the computers sold for $1,200. The most common sale price was The most common sale price was

$1,200. $1,200. Half of the computers sold for more Half of the computers sold for more

than $1,200. than $1,200. The difference between the highest The difference between the highest

and lowest sales price was $1,200.and lowest sales price was $1,200.

A

B

C

D

Box-and Whisker PlotsBox-and Whisker Plots

3 4 5 6 7 8 9

MIN Q1 MED Q3 MAX

Each of the quartile divisions represents 25% of the data.

Question 2:Question 2: The box-and-whisker The box-and-whisker plot below shows student scores plot below shows student scores

on a physical fitness test.on a physical fitness test.

Students receive an award for scores at or above the upper quartile. What is the lowest score a student can get to receive an award? Answer: 74

Question 3:Question 3: The box-and-whisker plot below The box-and-whisker plot below summarizessummarizes the test scores of an algebra class.the test scores of an algebra class.

Which of the following must be Which of the following must be true?true?

The median score is 70. The median score is 70. The lower quartile score is 50. The lower quartile score is 50. Half of the scores are between 60 and Half of the scores are between 60 and

75. 75. The interquartile range is half of the The interquartile range is half of the

range.range.

ABCD

USING THE TREND OF PAST USING THE TREND OF PAST DATA TO PREDICT THE FUTUE:DATA TO PREDICT THE FUTUE:

If you are analyzing a relationship If you are analyzing a relationship between TWO events (between TWO events (x x and and yy), you can ), you can use a use a line ofline of best fit (linear regression)best fit (linear regression) to predict the future. to predict the future.

How do you determine a How do you determine a line of line of best fit?best fit?

Use your calculator!Use your calculator!

Step 1:Step 1: Enter your Enter your data in Ldata in L11 and L and L2.2.

(STAT EDIT)(STAT EDIT)

xx yy

11 66

33 1111

44 11.511.5

66 1616

Step 2:Step 2: Determine the line of best fit.Determine the line of best fit.

STAT CALC: LIN REG (4)STAT CALC: LIN REG (4)

Then Then y = ax + by = ax + b

aa = 1.942307692 = 1.942307692

bb = 4.326923077 = 4.326923077

Be sure to fill in the Be sure to fill in the aa and and bb values! values!

yy = 1.942 = 1.942xx + 4.327 + 4.327

Use the line of best fit for Use the line of best fit for prediction:prediction:

What will be the What will be the yy value when value when xx = = 7 ?7 ?

yy = 1.942 = 1.942xx + 4.327 + 4.327 yy = 1.942 = 1.942(7)(7) + 4.327 + 4.327 yy = 17.921 = 17.921

A taxi company uses a formula to determine the fare. Let x represent the number of miles driven. Let y represent the total fare (in dollars) owed by the passenger. An equation for the line of best fit is:

y = .5x + 3

What is the slope of this line of best fit? What does the slope mean in the context of this problem?

What is the y-intercept of this line of best fit? What does the y-intercept mean in the context of this problem?

John has $10. How many miles can he travel by taxi?

The EndThe End