Chapter 3 DESCRIPTIVE STATISTICS FREQUENCY DISTRIBUTIONS Understanding Statistics

Chapter 3 DESCRIPTIVE STATISTICS: FREQUENCY DISTRIBUTIONS Understanding Statistics for International Social Work and Other Behavioral Sciences Serge Lee, Maria C. Silveira Nunes Dinis, Lois Lowe, and Kelly Anders (2015). Oxford University Press

FREQUENCY DISTRIBUTIONS Ø Frequencies. Typically, the term frequency distributions refer to raw scores, percent, valid percent, cumulative percent, and graphs or charts. § Percent or percentile is how people typically calculate percent for the variable. § Valid percent excludes missing data from the calculation. § Notice the denominator. Percent uses n while valid percent depends on valid n. § n = Sample size § Σ = Greek sigma for the sum of the variable § F = Frequency count 2

FREQUENCIES CONTINUED Cumulative percent is used to indicate position of a particular value. It is helpful to estimate the quartile range for ordinal data when the data set is large. Cumulative frequency and cumulative percent are helpful in professional practice. For example, 10 out of 200 workers have been with agency X for less then five years. By computation, 10/200 x 100% = 5%. The result shows that 5% of the workers have been with agency X for less than five years. Graphs/charts are included within frequency distributions because these figures are always accompanied with numerical scores, percentages, or both. 3

GRAPHS/CHARTS • Bar. Nominal data. Bars of graph do not touch each other. • Pie. Known as crossover. Can be used with any level of Fourmeasurement commonly used graphs are bar, thepie, but perhaps limit bars to five or less. Best with histograms, frequency polygons or line nominaland data. graphs. Use the following to build • Histograms. Interval orcriteria ratio data. Bars of graph touch but DO graph NOT cross each other. • Frequency polygons (line graphs). Similar to histograms. Requires interval or ratio data. Has advantage over histogram graphs due to the fact that several variables can be displayed on the same graph and the lines can crossover each other. 4

DIFFERENTIATE BETWEEN HISTOGRAM AND BAR Simple histogram graph 5 4, 5 4 3, 5 3 2, 5 2 1, 5 1 0, 5 0 Simple bar graph 25 20 15 10 5 Amount (in hour) of exercises per week Junior Freshman 0 Class standing Senior Sophomore Senior Junior Sophomore Freshman

DIFFERENTIATE BETWEEN FREQUENCY POLYGONS (LINE) AND BAR GRAPH Simple line graph Simple pie graph 100000 90000 87000 80000 70000 68000 60000 50000 54000 45000 40000 35000 30000 20000 35000 31000 16000 10000 0 24 36 32 Income 45 29 35 Work 27 47 31 Watch TV Play Do nothing 6