ch2 - organizing and presenting data
if you cant share your work with other people so they understand it, then what
was the point
- frequency distribution (table)
...how often does each data value appear
ex) is this your first semester at BMCC?
yes 12
no 10
frequency: total number of occurrences of a data value
relative frequency:
also: probability
when written "out of 100", its a percentage
note: relative freqencies add up to 1.
sometimes, because of rounding, that might not
happen on the chart
presenting qualitative data (words)
Bar Graph
ex) what is your major?
ex) # of people in poverty in Lower East Side
can include frequency labels
to be precise
-Pie Chart
ex) # of people with a particular major
label each slice with:
category; freq (or relative freq or
percentage)
note: if the textbook asks "how many
degrees in a slice?" ignore that - if you
need to be that precise, use software
presenting quantitative data
a frequency distribution (table) looks the same when each data value gets
its own frequency
when might it look different?
ex) what is your age?
31 19 22 33 25 32 22 51 21 20 21 22 31 26 43
break data up into data classes (from low to high)
(what class you choose is up to you)
here, break it up into 10s, 20s, 30s 40s 50s ...this is typical for dealing
with ages
each age range or "data group" is called a data class
the class width is the distance between classes
ex) here its 10 20-10=10 or 30-20=10
note: the class width must stay the same (in general)
the class limits (or class boundaries) are the highest and lowest values in the
class
(there are other technical definitions for this, we will use this simple one)
ex) what are the lower and upper class limits of the third data class?
how do you make a frequency distribution table with continuous data?
...adjust class limits according to your precision (number of decimal
places)
ex) if you record people's ages with 2 decimal places (20.47years, 21.65,
etc) then write your class limits with 2 decimal places: 10-19.99, 20-29.99,
30-30.99 etc
- histogram
..bar graph for quantitative data
# math classes
note: there is no gap between the bars
(some software programs get this wrong)
what if each class contains
several values?
ex) what about a graph for relative frequency?
note: for all these presentations,
anywhere you put frequency,
you can instead put relative frequency
(you get same shape, 1 replaced by 1/15 )
what if your data has a big gap?
ex) 19,22,56,20,21,27,32,22,47,25,24,42, 105,107,115,117,
* frequency polygon (line graph)
histogram, but instead of bars, connect
points with a line
10 20 30 40 50 60
* cumulative frequency graph (ogive: "oh-jive")
19,22,56,20,21,27,32,22,47,25,24,42
great for small data sets: it is visual
(like a histogram)
and it preserves all your data
ex) 105, 107, 112, 114
we can make:
bar graph using Excel / OpenOffice / StatDisk
pie chart using Excel / OpenOffice / StatDisk
histogram using StatDisk
there are lots of creative ways to represent data visually.
want to see a better visual representation we can all use? how about this NYC subway map:
http://www.kickmap.com/comparison/
for one guy, that creativity is his full-time job: http://www.informationisbeautiful.net/
this fellow tells the story of the world with animated statistics: http://www.youtube.com/watch?
v=jbkSRLYSojo
2.4 misleading representations
- a graph which is correct, but gives the wrong impression
> 3-dimensional pictures exaggerate the appearance of change
ex) money pile
* misleading graph
ex) salary graph
"look at the raises we give!"
short y-axis range - dont start from zero
exaggerates change
we can make:
bar graph using Excel / OpenOffice / StatDisk
pie chart using Excel / OpenOffice / StatDisk
histogram using StatDisk