Frequency Tables, Dot Plots, and Histograms

Objective: Add frequencies to find a sample size.

Prerequisite skills: counts and reading labeled tables. A frequency table records how many observations take each value or fall in each bin. The total sample size is the sum of frequencies, not the sum of the distinct values. Dot plots use one dot per observation. Common error: adding the values rather than the frequencies. Restrictions and interpretation: Frequency counts are not data values; histogram interval endpoints must be interpreted consistently.

Objective: Combine selected bins from a distribution.

To count observations meeting a threshold, add only the bins wholly within the requested range. If a threshold splits a histogram bin, the exact count may be unknowable from the grouped data alone. Common error: including bins below the requested cutoff. Restrictions and interpretation: Frequency counts are not data values; histogram interval endpoints must be interpreted consistently.

Objective: Compute a data sum from value-frequency pairs.

Each distinct value contributes value times frequency to the data total. Divide that total by the total frequency if a mean is requested. Histogram bin midpoints provide estimates rather than exact totals unless all data values are known. Common error: multiplying score labels together or taking an unweighted mean of labels. Restrictions and interpretation: Frequency counts are not data values; histogram interval endpoints must be interpreted consistently. Desmos and method choice: Use Desmos for arithmetic or a graph/table check when that reduces work. Enter parentheses explicitly and verify the requested quantity and units. Use the algebraic steps shown here for an exact result; a rounded graph display is not proof of exact equality.