Lesson 2: Dot Plots and Histograms

Property

A bar graph is used specifically for categorical data. It uses rectangular bars separated by gaps to represent the frequency of each category.
A valid bar graph requires a title, labeled axes, and a properly scaled vertical axis. Crucially, the vertical axis (y-axis) showing the frequency MUST start at 0. Starting the axis at a number greater than 0 visually distorts the proportions of the bars.

Examples

• Standard Bar Graph: A horizontal bar graph displaying favorite colors: Red (12 students), Blue (18 students), Green (8 students). The longer the bar, the more popular the choice. The categories are separated by gaps.
• The Zero-Axis Distortion: A graph shows votes for two candidates: Candidate A (52 votes) and Candidate B (48 votes). The true difference is very small. If the vertical axis starts at 40 instead of 0, Candidate A's bar will be 12 units tall and Candidate B's bar will be 8 units tall. This visually makes Candidate A look 50% more popular, misleading the reader.

Explanation

Bar charts are fantastic for comparing discrete groups, which is why there are visible gaps between the bars—the gaps signal that the categories don't bleed into one another. However, you must be a critical reader of graphs! The human eye naturally compares the total height of the bars. If a graph cuts off the bottom by starting the y-axis at a number like 50 instead of 0, it artificially stretches small differences to look like massive gaps.

Property

An easy graph to make for numerical data is called a dot plot.
To create a dot plot, first draw a number line and then place a dot above the number line at the location of each data value.
If a value is repeated, this is represented by placing another dot above the previous instance(s) of that value.
This type of graph allows us to identify clusters (data points together in a group), gaps (intervals without any reported values), peaks (data where there are more responses than for nearby values), and outliers (values that are significantly different from the rest of the data).

Examples

• A group of friends records the number of pets they own: 1, 0, 2, 1, 1, 3, 5. A dot plot would show a peak at 1, a cluster from 0-3, and a gap before the value at 5.
• Students' quiz scores are: 8, 9, 10, 7, 9, 9, 8. The dot plot for this data shows a peak at 9, indicating it's the most frequent score, and all data is clustered between 7 and 10.
• The number of goals scored in 7 soccer games was: 2, 3, 0, 1, 3, 2, 3. The dot plot has a peak at 3, showing it was the most common number of goals scored in a game.

Explanation

Dot plots are perfect for smaller sets of data. They let you see every single data point at a glance, making it easy to spot where data clumps together (clusters) or where the most common value is (peak).

Property

To construct a frequency table from a set of raw data:

1. Determine Intervals: Find the range of the data (maximum value - minimum value). Decide on a number of equal-sized, non-overlapping intervals that cover the entire range.
2. Tally Data: Go through the data set one value at a time. Make a tally mark in the row for the interval where each value falls.
3. Count Frequency: Count the tally marks for each interval and write the total in the "Frequency" column.

Examples