a 4 part statistics project

Review of Basic Statistics

 Classifying Data

o Qualitative Data  Consists of names or labels, categorical data

o Quantitative Data  Consists of numeric values, includes units of measurement

 Discrete o Only takes on countable values

 Continuous o Can take on any value within an interval

 Levels of Measure

o Nominal  Categories only, data cannot be arranged in order

o Ordinal  Data can be arranged in order, but differences either can’t be found or are

meaningless

o Interval  Differences are meaningful but there is no natural zero starting point and

ratios are meaningless

o Ratio  There is a natural zero starting point and ratios make sense

 Measures of Center

o Mean  The arithmetic average of all data points  =AVERAGE(data range)

o Median  The middle of an ordered data set  =MEDIAN(data range)

o Mode  The most frequently appearing data  First highlight several cells in a row, then enter =MODE.MULT(data

range) and then press Ctrl+Shift+Enter

o Mid-Range  The half-way point between the lowest and highest values  First find the maximum and minimum with =MAX(data range) and

=MIN(data range) and then enter =(Maximum+Minimum)/2

 Measures of Variation

o Range  The distance between the lowest and highest value  First find the maximum and minimum with =MAX(data range) and

=MIN(data range) and then enter =Maximum-Minimum

o Variance  Equal to the square of the standard deviation  =VAR.S(data range)

o Standard Deviation  A measurement of how far the data deviates from the mean  =STDEV.S(data range)

 Normal Distributions o A bell curve distribution whose shape is determined by a mean and a standard

deviation

o Standard Normal Deviations and 𝑧-scores  When the mean is 0 and the standard deviation is 1 it is called a standard

normal distribution. Measurements on this scale are identified by the

variable 𝑧

o Find a 𝑧-score  Find a z-score from a probability with =NORM.S.INV(probability)

 Note: z-scores are not percentages, do not change the decimal place when computing a z-score.

o Area and probability  Find a probability from a z-score with =NORM.S.DIST(z, TRUE)

 Parameters and Statistics

o A parameter is a measurement (usually a proportion, a mean, or a standard deviation) of an entire population. Usually these values are either impossible or

unrealistic to find.

o A statistic is a measurement used to estimate a parameter that is based on a sample taken from a population.

Measurement Parameter Statistic

Mean (average) Mu (𝜇) x-bar (�̅�) Proportion 𝑝 p-bar (�̅�)

Standard Deviation Sigma (𝜎) 𝑠 Variance Sigma squared (𝜎2) 𝑠2