Data Interpretation and Basic Statistics: Averages, Rates, Tables, and Graphs
Core skills
Measures of center summarize a data set. The mean is the sum of the values divided by the count; the median is the middle value after ordering the data, and with an even count you average the two middle values; the mode is the most frequent value, and a set may have none or several; the range is maximum minus minimum. When data appear in a frequency table, multiply each value by its frequency before adding, then divide by the total frequency. That is the same reasoning behind a weighted average, where each score counts in proportion to its weight. Rates compare quantities with different units, such as miles per hour, cost per ounce, or words per minute. Unit-rate problems are solved by dividing to find the per-one amount, then multiplying to scale up. When reading a table or graph, identify the title, the units, the scale of each axis, and the total before computing any percent.
Traps
Forgetting to order the data before locating the median; dividing by the number of distinct values instead of the number of data points; assuming the mean and median are close when outliers pull the mean; reading a graph against the wrong axis or ignoring a break in the scale; and computing a percent from a row total when the question asks for a percent of the grand total.
Worked example
For the data 4, 9, 7, 6, 9: the mean is (4 + 9 + 7 + 6 + 9) / 5 = 35 / 5 = 7; ordered (4, 6, 7, 9, 9) the median is 7; the mode is 9; the range is 9 - 4 = 5. Rule of thumb: sort the list first, then compute.