Statistics - The histogram

8/12/2019 Statistics - The histogram

1/37

STAT 2

Lecture 4:

The histogram


2/37

Review

If you can't do an experiment, maydo an observational study

Control for as many potentialconfounders as you can

Prospective studies are generallypreferable to retrospective studies


3/37

Review

With observational studies:

Quality of the study depends

heavily on quality of controls Causation is very difficult to

establish or define! "trong associations can be sho#n


4/37

Today

$ar graphs

"tem%and%leaf plots

&istograms:

% #hat are they

% ho# do you dra# them

% ho# do you interpret them


5/37

I

Graphing a variable


6/37

Types of variables

Categorical: favourite colour red,blue, green!

umerical discrete: die roll (, ),*, +, , -!

umerical continuous: #eight()*.*+ pounds, )((.- pounds!


7/37

Example: basketball scores

/* - ) 0+ - 0 00 -0 -/ ( 0+-- 11 0 0* -( -( -+ -- ) -0 -2

- * 02 -- / -( -- -0 - * 00*

3echnically discrete, but becausethere are so many possibilities,doesn't matter much if #e treat it

as discrete or continuous


8/37

Stem-and-leaf

3 5

4

5 261726383

6 578611467061675

7 4564307

8 3

9 9


9/37

Stem-and-leaf


10/37

Histogram


11/37

Histogram


12/37

Histogram/bar graph


13/37

hen to draw a!!!

&istogram: continuous data orgrouped numerical data

$ar graph: categorical data orungrouped discrete data

"tem%and%leaf: #hen you're in ahurry

Pie chart: controversial


14/37

II

Drawing a histogram


15/37

"rawing a histogram

Score Count

30-39 1

40-49 0

50-59 9

60-69 15

70-79 7

80-89 190-99 1


16/37

"rawing a histogram


17/37

"rawing a histogram


18/37

"rawing a histogram


19/37

#o$r t$rn

)220%)22/ Cal men's bas4etballscores:

-0 0+ 00 0+ /- ((0 0 0+ - (2) /-1) / 02 -1 12 0 00 -1 01 /( 020* 0- -1 +1 /+ /1 /2 /+ -- -/ -


20/37

#o$r t$rn


21/37

III

Histogram variations


22/37

%re&$ency vers$s percentage

Score Count Percent of total Height of block40-49 1 3 0.3

50-59 2 6 0.6

60-69 7 21 2.1

70-79 12 36 3.6

80-89 7 21 2.1

90-99 2 6 0.6

100-109 1 3 0.3110-119 1 3 0.3


23/37

%re&$ency vers$s percentage


24/37

How many blocks'

5ule of thumb don't follo# thisexactly!:

Number in sample Number of blocks9-16 5

17-32 6

33-64 7

65-128 8129-256 9

257-512 10

513-1024 11


25/37

(locks of $ne&$al width

In most cases, avoid these 3he &6I7&3 of the bloc4 gives

the percent per x%unit 3he 8568 of the bloc4 gives thepercent of the total that falls #ithinthe limits of the bloc4


26/37


Score Count Percent of total Height of block

40-59 3 9 0.5

60-69 7 21 2.1

70-79 12 36 3.6

80-89 7 21 2.1

90-119 4 12 0.4


27/37



28/37



29/37

I9

Comparing histograms


30/37

)omparing histograms

We may have additionalinformation that lets us divide the

data into groups ra# a histogram for each group

and compare them

3his is a 4ind of control


31/37



32/37



33/37

"escribing distrib$tions

Distribution: the set of values avariable ta4es, along #ith ho#

often the variable ta4es each value &ome distribution has a higher

centre than a#ay distribution

&ere, the t#o distributions havesimilar spreads


34/37

Recap


35/37

hen to draw a!!!

&istogram: continuous data orgrouped numerical data

$ar graph: categorical data orungrouped discrete data

"tem%and%leaf: #hen you're in ahurry

Pie chart: controversial


36/37

Recap

y%axis: can be frequency orpercentage

&eight of the bloc4 gives thepercent per x%unit

8rea of the bloc4 gives the percentof the total that falls #ithin thelimits of the bloc4

Tomorrow:


37/37

Tomorrow:;un #ith graphs

Statistics - The histogram

Documents

Transcript of Statistics - The histogram