Originally by "‘piccolojunior"’ on the College Confidential forums; reformatted/reorganized/etc by
Dillon Cower. Comments/suggestions/corrections: email@example.com
• Mean =x̄ (sample mean) = µ (population mean) = sum of all elements (
x) divided by
number of elements (n) in a set =
. The mean is used for quantitative data. It is a measure
• Median: Also a measure of center; better fits skewed data. To calculate, sort the data points and
choose the middle value.
• Variance: For each value (x) in a set of data, take the difference between it and the mean (x −µ
or x −x̄), square that difference, and repeat for each value. Divide the final result by n (number
of elements) if you want the population variance (σ2), or divide by n− 1 for sample variance
(s2). Thus: Population variance = σ2 =
. Sample variance = s2 =
• Standard deviation, a measure of spread, is the square root of the variance. Population standard
σ2 = σ =
. Sample standard deviation =
s2 = s =
– You can convert a population standard deviation to a sample one like so: s = σp
• Dotplots, stemplots: Good for small sets of data.
• Histograms: Good for larger sets and for categorical data.
• Shape of a distribution:
– Skewed: If a distribution is skewed-left, it has fewer values to the left, and thus appears to
tail off to the left; the opposite for a skewed-right distribution. If skewed right, median <
mean. If skewed left, median > mean.
– Symmetric: The distribution appears to be symmetrical.
– Uniform: Looks like a flat line or perfect rectangle.
– Bell-shaped: A type of symmetry representing a normal curve. Note: No data is perfectly
normal - instead, say that the distribution is approximately normal.
• Z-score = standard score = normal score = z = number of standard deviations past the mean;
used for normal distributions. A negative z-score means that it is below the mean, whereas a
positive z-score means that it is above the mean. For a population, z =