Week 3, Day 1: Chapter 18 (and 13) Data Interpretation

More from Ch. 13:

Frequency distributions – describe how often certain data values occur in sets and show these in tables, histograms, charts, and graphs, usually as percentages (but also as fractions or decimals).

 

Relative frequency – each frequency divided by the total number of data points; relative frequency distribution, aka probability distribution, shows this frequency in decimal form instead of percentage. Note that the total of relative frequencies is 100%, or 1 if using fractions or decimals.

 

Normal distribution – also known as the bell curve – here the mean will equal the median and mode and data are symmetrically distributed.

·       Standard deviation determines how spread out the curve is

·       The mean indicates how far from the axis (usually (0, 0) or origin on the coordinate graph) the center of the curve lies

 

Visual representations of data most frequently come in bar graphs, line graphs, pie charts, and tables. However, they work on the same principles as word problems, and ask the same kinds of questions.

·       Bar graphs

o   May be horizontal or vertical

o   Easily represent which values are greater or lesser

o   Requires estimation when measures fall between lines

·       Histograms

o   Special kind of bar graph showing relative frequencies

o   Y axis tends to show frequency

o   X axis can show many things – read carefully!

·       Segmented bar graphs (aka stacked bar graphs)

o   Special kind of bar graph showing multiple quantities on one bar

o   The different quantities sum to equal the whole bar

o   Taking one measure requires subtracting that quantity from the whole

o   Be very careful about calculations

·       Scatterplots

o   Dots scattered across the coordinate graph

o   Bivariate data, two measures related to each other on the x-y axes

o   Often given a trend line or regression line showing a central tendency which may be straight or curved

o   Pay close attention to the scales on each axis!

o   Useful for spotting outliers and standard deviation

·       Line graphs

o   Connect the dots with lines

o   Usually time plots or time series

o   Emphasize relative values

o   Scales matter here, too!

o   Gaps in the data are important

o   Time is usually given on the x axis

·       Pie charts (aka circle graphs)

o   Slices of a pie

o   Show distribution usually in percentages

o   Best for ratios

o   Not useful if the original number value of 100% = 100,000 or something is not given

·       Tables

o   Most accurate visual representation

o   Least easy to read

o   Prone to mistakes

o   Pay attention to column and row names

o   Useful for determining averages quickly

 

From Ch. 18: Data Interpretation

-        Based on information in tables and graphs

-        Often statistics-oriented questions

-        May be any answer type

Kaplan Method:

1) Analyze tables & graphs

            a) title – read

            b) scale – check units of measure & differences in axes

            c) notes – read carefully! Often critical

            d) key – read carefully

2) Strategy

            a) pay attention to detail – TAKE NOTES

            b) answer the right question!!! (in your notes, write down what you are seeking)

            c) practice sets increase in complexity, so do test sets

            d) look at answer choice formats before trying to solve

            e) approximate where possible

            f) SLOW DOWN and pace yourself

            g) practice, practice, practice