Data Analysis, Statistics, and Probability
Data Analysis
What this domain covers
Data Analysis questions ask you to read and interpret tables, bar graphs, line graphs, circle graphs, and scatter plots; to compare data sets; to spot trends and make predictions; and to judge whether a display is honest. You should be able to pull a specific value out of a two-way table, compute a total from percentages in a circle graph, and describe the relationship shown in a scatter plot as positive, negative, or none.
Reading a display carefully
Before answering, read the title, both axis labels, the scale increment, and any legend or key. Then locate the exact category or point the question names, not the one next to it. When a graph shows a trend, describe it in words first, then match your description to an answer choice.
Traps to watch for
- A vertical axis that does not start at zero, which exaggerates differences.
- Unequal intervals or a broken axis that distorts the picture.
- Circle-graph slices given as percentages that must be converted to counts.
- Confusing the total with a single category value.
- Choosing an answer that is true but does not answer the question asked.
Worked example
A student scored 78, 82, 74, and 78 on four tests and wants an 80 average over five tests. The five-test total must be 5 × 80 = 400. The four known scores total 312, so the fifth score must be 400 − 312 = 88. Rule of thumb: total equals mean times the number of values; use that to find a missing data point.
Statistics and Probability
What this domain covers
Statistics and Probability asks you to summarize a data set and to reason about chance. You need mean, median, mode, and range, plus an understanding of how outliers affect the mean more than the median. Probability questions cover simple events, sample spaces, theoretical versus experimental probability, and basic independent events, usually answered as a fraction, decimal, or percent.
Measures of center
Mean is the sum divided by the count. Median is the middle value after ordering the data; with an even count, average the two middle values. Mode is the most frequent value, and a set may have none or several. Range is maximum minus minimum. Always reorder the data before finding a median.
Traps to watch for
- Forgetting to sort the list before locating the middle.
- Ignoring an outlier that pulls the mean far from the median.
- Reporting a mode when no value repeats, or missing a second mode.
- Giving probability as a count instead of a fraction of the total.
- Mixing up and (multiply for independent events) with or (add for mutually exclusive events).
- Forgetting that all probabilities in a sample space sum to 1.
Worked example
For the data set 3, 7, 7, 9, 14: the mean is 40 ÷ 5 = 8; the median is 7; the mode is 7; the range is 14 − 3 = 11. If a bag holds 4 red and 6 blue marbles, the probability of drawing red is 4 out of 10, or 2/5, equal to 0.4 or 40 percent. Rule of thumb: probability of an event equals favorable outcomes divided by total possible outcomes.