Read and interpret frequency tables and dot plots.
Reading exact values, totals, and medians from frequency tables and dot plots.
Core Idea
A frequency table lists values and how often each appears. A dot plot does the same thing visually — each dot is one data point stacked above its value on a number line.
Understanding
A frequency table has two columns: the value and the count (frequency). To find the total number of data points, add the frequency column. To find the median, count into the ordered list until you hit the middle position.
A dot plot is a frequency table turned sideways. Each dot represents one observation. A stack of 4 dots above the number 3 means the value 3 appears 4 times.
The key skill is positional counting. If a table shows 20 total observations, the median is the average of the 10th and 11th values when listed in order. Count through the frequencies from left to right until you land on those positions.
SAT dot-plot questions usually test whether you can extract exact values — total count, frequency of a specific value, or the median. Skim the dots left to right and keep a running total of positions.
Step by Step
- Read each value and its frequency from the table or dot plot.
- Add all frequencies to find the total number of data points
𝑛 - To find the median: if
𝑛 𝑛 + 1 2 𝑛 𝑛 2 𝑛 2 + 1 - Count through frequencies from the smallest value upward until you reach the target position.
Misconceptions
- Counting dots incorrectly when they're tightly packed — slow down and count each column separately.
- Forgetting to average the two middle values when
𝑛 - Confusing frequency (how many times a value appears) with the value itself.
Worked Example
A dot plot shows the number of hours 16 students spent studying for a test. The dots are distributed as follows: 2 dots above 1, 3 dots above 2, 3 dots above 3, 4 dots above 4, 2 dots above 5, and 2 dots above 6. What is the median number of hours spent studying?
Select an answer to see the explanation