Data Analysis and Probability
The Data Analysis and Probability domain asks you to represent and interpret numerical data, especially on line plots that use fractional values. Grade 5 FAST items typically show data in a table, line plot, or bar graph and ask for the median, mode, or range, or ask you to compare two data sets. Probability questions use simple equally likely outcomes and express likelihood as a fraction.
Reading line plots
- Each X represents one data value; the scale may be marked in fourths or eighths.
- Count the Xs above each value to build a frequency table before computing any measure.
- The total number of Xs is the number of data points.
Measures of center and spread
- Median: arrange values from least to greatest. With an odd number of values, take the middle one. With an even number, average the two middle values.
- Mode: the value that occurs most often. A set may have no mode or more than one mode.
- Range: the greatest value minus the least value; it measures spread, not center.
Probability
For equally likely outcomes, probability = favorable outcomes ÷ total outcomes. A bag with 3 red and 5 blue marbles gives P(red) = 3/8. Probability ranges from 0 (impossible) to 1 (certain).
Worked example
A line plot shows these seven values: 1/4, 1/2, 1/2, 3/4, 3/4, 3/4, 1.
- Median: the fourth value in order is 3/4.
- Mode: 3/4 appears three times, more than any other value.
- Range: 1 − 1/4 = 3/4.
Traps that cost marks
- Counting the number of different values instead of the number of Xs when finding the median.
- Forgetting to order the data before locating the median.
- Calling the greatest value the range; range is a difference.
- Misreading a fractional line-plot scale by counting tick marks from the wrong endpoint.
- Writing probability as a ratio of favorable outcomes to unfavorable outcomes instead of to total outcomes.