Topic 2: Frequencies & distributions

Frequency Tables

List measurement categories (X) and their corresponding

frequencies ( f ).

Proportion ( p )

The fraction of the total group associated with each score

(p = f/n).

Percentage

The proportion multiplied by 100 (p x 100).

Real Limits

Boundaries for intervals of continuous scores (e.g., a score of

67" has real limits of 66.5 and 67.5).

2.1 introduction summary

A frequency distribution organizes a data set by tabulating the number of

individuals located in each category on the scale of measurement.

Symmetrical

One side is a mirror image of the other.

Positively Skewed

The tail points toward the positive (right) end of the

x-axis

Negatively Skewed

The tail points toward the negative (left) end of the

x-axis.

2.2: Percentiles and Percentile Ranks Summary

Although a distribution shows the overall shape of a sample, percentiles and ranks allow us to describe the exact position of an individual score relative to the rest of the group.

Percentile Rank

The percentage of individuals in the distribution with scores equal to or less than a particular value. (eg: If a score of 1215 has a percentile rank of 75, then 75% of the population scored 1215 or lower.)

Percentile

The specific raw score (X) identified by its rank. (eg: The "75th percentile" is the score of 1215.)

Cumulative Frequency ( cf )

The number of scores at or below a specific value. The top of this column should always equal n (total sample size).

Cumulative Percentage ( c% )

The percentage of individuals accumulated up

to the top of a specific interval (formula: c% = (cf/n) x 100.)

Discrete/Ordinal Scales

You can only identify percentiles that appear directly in your table. If a rank (like the 40th percentile) isn't listed, you cannot "calculate" it because the values between categories (like 2.5) don't exist on these scales.

Continuous/Grouped Scales

For variables like height, weight, or exam scores, we can estimate values that fall between the scores listed in the table using interpolation.