7.7 Statistics & Statistical 7.7 Statistics & Statistical GraphsGraphs

p.445p.445

What are measures of central tendency?

How do you tell measures of central tendency apart?

What is standard deviation? How is it calculated?

What are the part s of a box-and-whiskers plot? How do you find them?

When is a box-and-whiskers plot useful?

What are the parts of a frequency distribution?

How do you draw a histogram? Why?

An intro to StatisticsAn intro to 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 3 we will be using. Tells you what the “center” of the data is.

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 2 middle numbers, the median will be the average of those 2.

Mode – the number(s) that occur most frequently. It is possible to have more than 1 mode or even no mode.

Ex: Find the mean, median, & mode of Ex: Find the mean, median, & mode of the following set of numbers: 36, 39, 40, the following set of numbers: 36, 39, 40,

34, 48, 33, 25, 30, 37, 17, 42, 40, 24.34, 48, 33, 25, 30, 37, 17, 42, 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

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

Ex: 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

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

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 info below a number line.

• Draw the box and whiskers.

Frequency DistributionFrequency Distribution

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.

Another way to show the same Another way to show the same info. is in a info. is in a histogramhistogram..

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!

What are measures of central tendency?Mean, medium and modeHow do you tell measures of central tendency apart?Mean=average, median=middle, mode=appears most oftenWhat is standard deviation? How is it calculated?Standard deviation=typical difference between the mean and a

data value. Use the formula on page 446.What are the parts of a box-and-whiskers plot? How do you find

them?Median, maximum and minimum values, upper and lower quartiles

on a number line. Lower quartile=median of the lower half. Upper quartile=median of the upper half.

When is a box-and-whiskers plot useful?Good for comparing median data.What are the parts of a frequency distribution?Intervals, tallys and frequencyHow do you draw a histogram? Why?Bar graph with bars touching because data values are continuous.

Assignment

Page 449, 12-30 every 3rd problem, 33-35, 43-45