Box plot analysis
The box plot
is a graphical representation of data that shows a data set’s lowest value,
highest value, median value, and the size of the first and third quartile. The
box plot is useful in analyzing small data sets that do not lend themselves
easily to histograms. Because of the small size of a box plot, it is easy to
display and compare several box plots in a small space. A box plot is a good
alternative or complement to a histogram and is usually better for showing
several simultaneous comparisons.
How to
use it: Collect and arrange data. Collect the data and arrange it into an ordered set from lowest value to
highest. Calculate the depth of the median. d(M) = where d =M = n =2depth; the number
of observations to count from the beginning of the ordered data set
median
number of observations in the set of data
If the
ordered data set contains an odd number of values, the formula will identify
which of the values will be the median. If the ordered data set contains an
even number of values, the median will be midway between two of the values.
Calculate
the depth of the first quartile. d(Q1) = (1)n
2
where d =(Q1) = n =4depth; the number of observations to count from the
beginning of the ordered data set
the first quartile
number of observations in the set of data
where d =(Q1) = n =4depth; the number of observations to count from the
beginning of the ordered data set
the first quartile
number of observations in the set of data
The first
quartile will be the value of the data item identified by this formula. Calculate
the depth of the third quartile. d(Q3) = (3)n 2
where d =(Q3) = n =4depth; the number of observations to count from the beginning
of the ordered data set the third quartile number of observations in the set of
data
where d =(Q3) = n =4depth; the number of observations to count from the beginning
of the ordered data set the third quartile number of observations in the set of
data
The third
quartile will be the value of the data item identified by this formula.
Calculate
the interquartile rage (IQR). This range is the difference between the first and third quartile vales.
(Q3 - Q1)
Calculate
the upper adjacent limit. This
is the largest data value that is less than or equal to the third quartile plus
1.5 X IQR. Q3 + [(Q3 - Q1) X 1.5]
Calculate
the lower adjacent limit. This
value will be the smallest data value that is greater than or equal to the
first quartile minus 1.5 X IQR. Q1 - [(Q3 - Q1) X 1.5]
Draw and
label the axes of the graph. The
scale of the vertical axis must be large enough to encompass the greatest value
of the data sets. The horizontal axis must be large enough to encompass the
number of box plots to be drawn.
Draw the
box plots. Construct the
boxes, insert median points, and attach upper and lower adjacent limits..
Identify outliers (values outside the upper and lower adjacent limits) with
asterisks.
Analyze
the results. A box plot
shows the distribution of data. The line between the lowest adjacent limit and
the bottom of the box represent one-fourth of the data. One-fourth of the data
falls between the bottom of the box and the median, and another one-fourth
between the median and the top of the box. The line between the top of the box
and the upper adjacent limit represents the final one-fourth of the data
observations. Once the pattern of data variation is clear, the next step is to
develop an explanation for the variation.
A segment
inside the rectangle shows the median and "whiskers" above and below
the box show the locations of the minimum and maximum.
This simplest
possible box plot displays the full range of variation (from min to max), the
likely range of variation (the IQR), and a typical value (the median).
Not uncommonly real datasets will display surprisingly high maximums or
surprisingly low minimums called outliers.
This simplest
possible box plot displays the full range of variation (from min to max), the
likely range of variation (the IQR), and a
typical value (the median). Not uncommonly real datasets will display
surprisingly high maximums or surprisingly low minimums called outliers.
•
Outliers
(Extreme outliers) are
either 3×IQR or more above the third quartile or 3×IQR or more
below the first quartile.
Suspected
outliers (Outliers) are
slightly more central versions of outliers: either 1.5×IQR or more above
the third quartile or 1.5×IQR or more below the first quartile.
Sonam Doma Lama
Group : G
Refrences :
http://web2.concordia.ca/Quality/tools/4boxplots.pdf
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