# Biostatistics

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```					            Biostatistics
Unit 3 - Graphs
Grouped data
Data can be grouped into a set of non-overlapping,
contiguous intervals called class intervals
(bins). Class intervals are used to sort the
data. Between 6 and 15 class intervals are usually
used depending on the range of the data.
Grouped data

The frequency tells how many of the data
values fall into each class interval. Frequency
can be displayed graphically using the
histogram and the frequency polygon.
Bacterial cell lengths
Below are the measured lengths of 30 individual
bacterial cells. As they have not yet been sorted to
make a sorted list, they can be considered as raw
data.
1) 1.5     2) 2.0      3) 2.0     4) 3.0      5) 2.0
6) 3.2     7) 2.3      8) 1.5     9) 2.0     10) 2.0

11) 1.0    12) 1.0     13) 2.5    14) 3.4     15) 2.1
16) 2.0    17) 4.0     18) 3.0    19) 2.0     20) 2.0

21) 2.2    22) 2.0     23) 2.0    24) 2.0     25) 2.0
26) 1.5    27) 2.0     28) 1.0    29) 1.0     30) 1.0
Basic statistics
The values of the basic statistics for the data are
presented below. They were obtained using the TI-
83 calculator. Similar results are available using
Microsoft Excel.
n = 30          min x = 1.0
mean = 2.04      Q1 = 1.5
s = .7186        median = 2.0
mode = 2.0       Q3 = 2.2
range = 3.0      max x = 4.0
Frequency Table for Bacterial
Cell Lengths
Class interval ( m )   Frequency
0.50 - 1.49              5
1.50 - 2.49             19
2.50 - 3.49              5
3.50 - 4.49              1
Histogram
Frequency Polygon
Percentiles and quartiles
Percentiles are used for location of data on the
horizontal axis. The median corresponds to the 50th
percentile. We generally are interested in quartiles
which are 25th percentiles. The first quartile (Q1) is
the 25th percentile. It contains one-quarter of the
data. The second quartile is the median which
marks the point with half of the data.
(continued)
Percentiles and quartiles
The third quartile (Q3) is the 75th percentile
representing three-quarters of the data. Using our
ordered observations, the quartiles are calculated
using the formulas below.
The interquartile range is represented by Q3 - Q1.
Calculation of quartiles
For the data set of 30 observations of bacteria, this
means that:

Q1 = (n+1)/4 -> 7.75 --> 8th observation (1.5)

Q2 = 2(n+1)/4 ->15.5 --> average of the 15th and
16th observations (2.0)

Q3 = 3(n+1)/4 -> 23.25 --> 23rd observation (2.2)
(continued)
Calculation of quartiles
Be careful when interpreting quartile
calculations. An answer of Q1 = 7.75 rounded
to 8 does not mean that the first quartile is
8. It means that the first quartile is the data
item in the 8th position. In this data set that
value is 1.5.
Box Plot
•The box plot is used to convey information
about the data. It makes use of the quartiles
that were calculated above.
1. Draw a number line representing cell
length on the horizontal axis.
2. Above the horizontal axis draw a
rectangle with the left-hand end of the
rectangle directly above Q1 and the right-hand
end of the rectangle directly above Q3.
Box Plot
3. Draw a vertical line across the box directly over
Q2.

4. Draw a horizontal extension line out of the left-
hand end of the box to a point above the smallest
measurement of the data. At this point draw a
vertical line.

5. Draw another horizontal line out of the right-
hand end of the box to a point above the largest
measurement of the data. Draw a vertical line at this
point.
Box plot of cell measurements
fin

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 views: 0 posted: 11/5/2012 language: English pages: 16
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