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Exploring Data: Statistics & Statistical

GraphsDuring this lesson, you will organize data by using tables and graphs.

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Organizing DataOrganizing Data

Data- information, facts, or numbers that describe something

A collection of data is easier to understand when it is organized in a

table or graph. While there is no “best way” to organize such data; there are many good ways. This lesson illustrates several types of

tabular and graphic representations.

Tables, frequency distributions, line plots, histograms, circle graphs, and pictograms are all

ways to represent data.

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REVIEW: Statistics

Statistics – numerical values used to summarize & compare sets of data (such as ERA in baseball).

Measures of Central Tendency – mean, median, & mode are the three “averages” which we will be using

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Mean – ( x ) average of n numbers (add all #s & divide by n)

Median – the middle # when the #s are written in order from least to greatest or greatest to least. If there are two middle numbers, the median will be the average of those numbers.

Mode – most frequently occurring number. NOTE: It is possible to have more than 1 mode or even no mode.

Three “Averages”

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EXAMPLE: EXAMPLE: Find the mean, median, & Find the mean, median, & mode of the following set of numbers: mode of the following set of numbers: 36, 39, 40, 34, 48, 33, 25, 30, 37, 17, 36, 39, 40, 34, 48, 33, 25, 30, 37, 17,

42, 40, 2442, 40, 24..

MeanMean - 445 13

MedianMedian – Put the numbers in order first!

17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40, 42, 48

ModeMode – most frequent! 40 is the mode.

2.34

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Measures of DispersionMeasures of Dispersion – tell how spread out the data are

* Range – difference between the largest and smallest values.

(for example: the range of the last example would be 48-17=31)

* Standard Deviation - (σ – “sigma”)

n

xxxxxx n22

22

1 )(...)()(

x1, x2, x3, …, xn are the entries in the data set.n is the number of entries in the set

x is the mean

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EXAMPLE: Find the standard deviation of the data from the first

example.

13

)2.3424(...)2.3440()2.3439()2.3436( 2222

13

32.856

87.65

12.8

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EXAMPLE: EXAMPLE: Box-and-whisker plotsBox-and-whisker plots

0 10 20 30 40 500 10 20 30 40 50

Minimum value

(17) Median (36)

Maximum value

(48)Lower Quartile – median of all

numbers in the list to the left of

the median

(25+30)/2 = 27.5

Upper Quartile – median of all

numbers to the right of the median

(40+40)/2 = 40

BoxWhisker Whisker

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Hints for making a Hints for making a box-and-whiskers plot:box-and-whiskers plot:

Make sure data is in order from least to greatest.

Find the minimum value, median, maximum value, upper & lower quartiles.

Plot the points for this information below a number line.

Draw the box and whiskers.

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EXAMPLE: EXAMPLE: Frequency Frequency DistributionDistribution

Title Goes Here

Interval Tally Frequency

0 to 9   0

10 to 19  l 1

20 to 29  ll 2

30 to 39  llll l 6

40 to 49  llll 4

Assign appropriate

intervals that will include all data values in

the set.

Put a tally mark for each data value in

the appropriate

row.

Count the number of tally marks and put the total in the last column.

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EXAMPLE:EXAMPLE: Histogram Histogram

6

5

4

3

2

1

0

TITLE HERETITLE HERE

0 - 9

10 -

19

20 - 29

30 - 39

40 - 49

LABEL HERELABEL HERE

L L A A B B E E LL

H H E E R R EE

Intervals

Frequency Bars should be

touching!

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Final Checks for Understanding

1. Give an example of a collection of data that you could organize using a box-and-whiskers plot.

2. Your classmates were asked to select their favorite type of music from these choices: classical, jazz, country, rock, and rap. How would you organize the results?

3. Which technique do you think is best suited to organize the results of a student council election?

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Homework Assignment: