Frequency Tables and Their Statistics

1
Frequency Tables and Their Statistics
2
Percentiles

• Percentiles give the percent (usually expressed
  as a WHOLE number) of data cases below a given
  case.
• For example if 38 percent of the scores, in a
  distribution of scores, is BELOW Mortimers score
  of 72 then in that distribution of scores, 72 is
  equivalent to the 38th percentile.
• Generally we would say that the Percentile Rank
  (PR) for a raw score of 72 is 38PR

3
Percentiles and Cumulative Frequencies

• Percentiles can be read directly from the
  cumulative frequency column in an SPSS frequency
  table.
• In this table, the PR for a score of 6 is 20 for
  a score of 8 it is 56.

4
Quartiles

• Certain percentiles are particularly important
  and are given special names
• The 25th percentile is know as the 1st quartile.
• The 50th percentile is the 2nd quartile AND is
  also know as the median.
• The 75th percentile is the 3ed quartile.
• The difference between the 1st and 3ed quartile
  is know as the inter-quartile range.

5
Reading Quartiles form Frequency Tables

• In the table, a score of 6 is at the 1st quartile
  (25th percentile).
• A score of 10 is at the 3ed quartile (75th
  percentile).
• What score is at the median?

6
Skew

• Indicates the extent to which a distribution
  deviates from symmetry around the mean of the
  distribution.
• Positive Skew More scores are LOWER than the
  mean the distribution has a long tail in the
  direction of higher scores (to the right)
• Negative Skew More scores are higher than the
  mean long tail to the left.

7
Kurtosis

• Indicates the flatness or peakedness of a
  distribution.
• Leptokurtic distributions are peaked (scores tend
  to be tightly packed around the mean).
• Platakurtic distributions are flat (scores tend
  to be more evenly spread out).
• Mesokurtic distribution tend toward normal
  distributions.