Frequency distribution table

1. An organized tabulation of the number of individuals located (distributed) in each category on the scale of measurement (shows in a table or graph).
1. The set of categories that make up the original measurement scale.
2. A record of the frequency, or # of individuals in each category.

1. Proportion (p): Measures the fraction of the total group that is associated with each score. p = f/N -> also called relative frequencies.

2. Percentage: p • 100

1. A frequency distribution where scores are grouped into intervals rather than listed as individual values.
1. Class intervals: groups/range of scores in a grouped frequency distribution; each table should have about 10 intervals that have same widths of simple numbers (2, 5, 10, 20) and bottom score that are multiples of the chosen width. Also, each interval shouldn't have gaps and overlaps.
• Example of bottom score: [50, 54] with width of 5, bottom score would be 50. Both values are apparent limits.
• The real limits of the interval would be the real limits of the apparent limits -> [49.5, 54.5] (still width of interval)
• Do from
• Calculating amount of rows = highest # - lowest # + 1
2. Limitations: Information is lost the longer the width of intervals because we don't know how many people get a specific score.

What is the purpose of a grouped frequency distribution table?

1. Histogram: For interval or ratio scales. A graph showing a bar above each score/interval so the height corresponds to the frequency and width extends to real limits. Shows distribution of sample. No spaces or gaps between bars. Easy for the general public to understand.
2. Polygon: For interval or ratio scale. A graph consisting of a continuous line that connects a series of dots placed above each score so that the height of the dot corresponds to the frequency. Easy for the general public to understand.
1. Dots are put at the midpoint of each interval.
3. Bar graphs: For nominal or ordinal scales. A graph showing a bar above each score/interval so that the height of the bar corresponds to the frequency. A space is left between adjacent bars. Used in professional publications
4. Line graphs: For continuous variables. Most common graph type used for correlational linear relationships. Can be one line or two to show group comparison. Used in professional publications. (never use pie charts -> hard to read).

1. Describe the basic elements of a frequency distribution graph and explain how they are related to the original set of scores.

1. X-axis for measurement size and y-axis for frequency
2. Y-axis is 2/3 or ¾ of x-axis
3. Value of 0 for both x- and y-axis at intersection

Explain how frequency distribution graphs for populations differ from the graphs used for samples.

Relative frequencies: For nominal and ordinal scales. What you get when you calculate the proportion of the total distribution. If shown in a graph, you can estimate that one category is greater than the other by putting a longer bar on a bar graph (exact # not specified).

Smooth (or normal) curves:  For interval and ratio scales. Making a smooth curve that shows the relative changes that occur from one score to the next without connecting a series of dots (real frequencies). Shape is symmetrical with high frequencies in the middle and low on the sides.

1. Symmetrical: being possible to draw a vertical line through the middles so that one side of the distribution is a mirror image of the other.
2. Skewed: The scores tend to pile up towards one end of the scale and taper off gradually at the other end. Provides a general idea of the distribution; can be "roughly symmetrical" or "tends to be positively skewed."
1. Positively: where the scores decrease (tail of the distribution) on the right/positive side of the x-axis.
2. Negatively: where the tail points to the left.

1. Percentiles: A score identified by a percentile rank (ex. 95th percentile). Tells us that 95% of scores are lower than this score. C% shows percentiles.
2. Percentile rank: A particular score defined by the percentage of individuals in the distribution with scores at or below the particular value. Tells us that 75% of people scored lower.

1. Cumulative frequencies (cf): Use the table and count # of scores at or below each category, accumulating individuals as you move up the scale.
1. Shows total f ( or p or %) at each value and all lower ranked values (relative standing)
2. Cumulative percentages (c%): converting the cumulative frequencies of each category into percentages to find percentiles. The percentage only applies to the upper real limit of each category. So if X = 1, the percentile is actually 1.5.
1. Or you can add up the % next to proportion.

1. Interpolation: used to estimate intermediate values within an interval by assuming that fractional portions of one scale correspond to the same fractional portions of the other scale.
1. Assumes there's a constant rate of change
2. Use upper real limits for grouped frequency

1. Stem and leaf display: Simple alternative to a grouped frequency distribution table or graph.
1. Each score is separated into two parts: first digit(s) -> stem (correspond to class interval); last digit -> leaf
2. Allows you to see every individual score in the data.