Data Analysis and Probability
Data Analysis and Probability tests your ability to read displays, summarize a data set, and quantify chance. You need to choose the measure that answers the question, not just calculate every measure you know.
Displays
- A line plot shows frequency along a number line, including fractional values; each mark represents one data point.
- A bar graph compares categories; check the scale, labels, and intervals before reading values.
- A frequency table counts how often each value occurs and can be used to build a line plot or bar graph.
Measures of center and spread
- Mean = sum of values ÷ number of values; it is the fair-share value.
- Median = middle value when the data are ordered; with an even count, average the two middle values.
- Mode = most frequent value; a set may have no mode or more than one.
- Range = maximum − minimum; it measures spread, not center.
- Outliers pull the mean more than the median.
Probability
- P(event) = number of favorable outcomes ÷ total number of equally likely outcomes.
- Probability ranges from 0 to 1; the complement of an event has probability 1 − P(event).
- Experimental probability comes from results; theoretical probability comes from equally likely outcomes. Larger samples tend to come closer to theoretical probability.
Worked example
Data set: 3, 7, 7, 9, 14. Sum = 40, count = 5, mean = 8. Ordered data give median = 7. Mode = 7. Range = 14 − 3 = 11. If 14 is replaced by 34, the mean becomes 60 ÷ 5 = 12, but the median stays 7 because the middle value has not changed.
Traps that cost marks
- Finding the median without ordering the data first.
- Treating the mean and median as interchangeable.
- Using the wrong denominator in a probability fraction.
- Counting outcomes that are not equally likely as if they were.
- Misreading a graph because the scale jumps by 2, 5, or 10.
- Forgetting that range describes spread, not a typical value.