Here is some data
Here is some data. Find upper and lower quartile, and the median.
|43 |51 |53 |55 |57 |58 |58 |59 |60 |61 |
|61 |61 |61 |61 |62 |63 |64 |64 |65 |65 |
|65 |66 |66 |66 |66 |66 |66 |67 | | |
For the above example:
Location of Median:
Location of Lower Quartile =
Location of Upper Quartile =
Median:
Lower Quartile Q1 =
Upper Quartile Q3 =
These descriptors of data can be used to construct a very informative graph, called Box and Whiskers Plot, or Skeleton Box Plot, or just Box Plot.
How to construct a Box Plot
1. Find the median, lower and upper quartile
2. Find the range of the data
3. Draw a straight line, and a reference line, which goes from the smallest to the largest number
4. Draw three vertical lines: one at the lower quartile, one at the median, and one at the upper quartile.
5. Turn those three lines into a box.
Example: For the above data we had: lower quartile = 58.5, median was 61.5, upper quartile was 66.5, range was 67 - 43 = 24. The corresponding box plot looks like:
[pic]
What the Box Plot tells you:
1. The median and the quartiles
2. The lowest and highest measurement, hence also the range
3. Whether the corresponding frequency histogram is mount-shaped or skewed.
4. What the estimated standard deviation is (if close to mound-shaped)
5. Whether mean is less than median or larger (depends on skewness)
6. What the corresponding frequency histogram would look like
Here are a couple of box plots, and you are supposed to answer the 6 questions above.
[pic] [pic]
[pic]
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