FIELDSTON BIOLOGY
STATISTICS SUMMARY PACKET
TOOL
MEAN
DESCRIPTION
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Average, sum of a set of data divided by the number of data
When to Use: use to describe the middle of a set of data – most useful when data set does not have outliers or is not skewed
to one extreme
Useful when comparing sets of data
Affected by extreme values or outliers
Example: 4, 5, 6, 5, 4 Mean: (4 + 5 + 6 + 5 + 4) / 5 = 4.8
MEDIAN
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Middle value, or the mean of the middle two values, when the data is arranged in numerical order
When to Use: use median to describe middle of set of data, more helpful when there are outliers or data is skewed
Useful when comparing sets of data
Not as affected by extreme values or outliers
If the numbers in the data are more clustered, without outliers or skewed data, the mean provides more information than
median
Example: 4, 5, 6, 5, 4 Median: 4, 4, 5, 5, 6 = 5
MODE
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Value, or number, that appears the most; it is possible to have more than one value or for no mode to exist
When to Use: use mode when the data are non-numeric or when asked to choose the most popular item
Not as affected by outliers or skewed data
When no values repeat in data set, mode is every value and not useful
When there is more than one more, difficult to interpret and/or compare
Example: 4, 5, 6, 5, 4 Mode = 4 and 5
DISTRIBUTION NORMAL DISTRIBUTION VS SKEWED DISTRIBUTION
OF DATA:
Normal
Distribution
Skewed
Distribution
Outliers
NORMAL DISTRIBUTION:
 In normal distribution, extremely-large values and extremely-small values are rare. Most-frequent values are clustered
around the mean (which here is same as the median and mode).
SKEWED DISTRIBUTION:
 When data is shifted to one extreme, may be due to a real phenomenon that you are studying in your experiment. Another
statistical tool (line of best fit) may be helpful in demonstrating that the skewed pattern is REAL, and not due to chance.
 Not necessarily the same thing as outliers
OUTLIERS:
 an observation that is numerically distant from the rest of the data
 can occur by chance in any distribution but are often indicative of a measurement error
 no rigid mathematical definition of what constitutes an outlier --> ultimately determination is subjective and must be
discussed openly
 if mean = (or close to) median, then probably no outliers
 if mean is not close to median, then most likely due to outlier
 often you will “know one when you see one”
 Estimators capable of coping with outliers are said to be robust: the median is a robust statistic, while the mean is not.
How to Deal with OUTLIERS (Not Necessarily SKEWED DATA):
 If you can identify a concrete reason for why this outlier occurred then you can simply throw it out
 WHEN TO THROW OUT DATA, examples:
 if one group performed their experiment on a different day than the rest of the groups where the conditions of the
experiment were affected by running it on a different day (ex, using reactive solutions that are a day older)
 if the group with the outlier noted that they had spilled some of their solution, then you could throw out their data.
 CAUTION: whatever criteria you used to throw out piece of data, that criteria must be applied to ALL other groups.
 EX: a procedure called for you to keep the solutions at 23 degrees C. So if you threw out data from a group because they
performed the experiment at 33 degrees C, then you must throw out any data that was obtained at 33 degrees, even if
that data “looks good”
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ACCURACY
vs
PRECISION
If you can’t find legitimate way of eliminating an outlier, you can always perform statistical analysis WITH and WITHOUT the
outlier included AND include both analysis. You could describe how while data did not support your hypothesis, if you
eliminate this one outlier it changes the data enough to support your hypothesis.
Accuracy: how close a measured value is to the actual (true) value
Precision: how close the measured values are to each other
If you are playing soccer and you always hit the left goal post instead of scoring, then you are not accurate, but you are precise!
ERRORS
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Systematic Error: impacts accuracy of experiment; errors that may be reduced by some form of modification to the
experimental design or execution
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Random Error: impacts precision of experiment; reduce the effect by averaging multiple trials
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ROUNDING
Experimental Design / Method Error
 Errors in underlying assumptions in how the DV is being measured
Human Error: ex., put in 2 drops when 3 drops were called for
Instrumental Error
Ex., balance that is calibrated correctly but gives two different measurements
When calculating, rounded value should not go beyond the precision of instrument that was used to record.
If last value is between 1 – 4  Round down; If last value is between 5 – 9  Round up
Example: 3.15 + 2.7 + 1.624 = 7.474  7.5
% CHANGE
Describes the amount of change relative to the original value.
(Final – Initial)/Initial * 100
Example: Initial = 2 grams, Final = 3 grams
% Change: (3 – 2) / 2 * 100 = 50%
ABSOLUTE
AVERAGE
DEVIATION
Absolute Average Deviation tells you the average spread (range) of the numbers around the mean of a sample. In order to calculate
the absolute average deviation, you:
1. Take the difference between each score relative to the mean
2. And then take the absolute value average of all the deviations
The value you get represents the spread, or range, of your data.
% ABS AVE % in which the Absolute Average Deviation is relative to the Mean = (ABS AVE DEV / MEAN) * 100
DEV
RELATIVE TO Example: MEAN = 30, ABS AVE DEV = 5
% the ABS AVE DEV relative to Mean = (5/30) *100 = 16.7%
MEAN
T TEST
When to use:
 when comparing two or more different data sets, t test helps us to see if two data sets are different enough from each other
so that we don’t think they are different due to chance. If they are different enough, we say the difference is statistically
significant
 Calculation takes into consideration both difference in means as well as range/deviation within each data set