Line Plots and Dot Plots - Algebra-1

1. Fundamental Concepts

Definition: Line plots and dot plots are statistical graphs used to display data distribution. They present the occurrence of data by marking points or lines on a number line (or category axis).
Function: Visually reflect the central tendency, distribution range, and specific values of individual data, suitable for displaying small-scale datasets.
Components: Include a number line (to represent the range of data values) and corresponding data points (each point represents the occurrence of a data value).

Minimum: The smallest value in a dataset.
Maximum: The largest value in a dataset.
Range: The difference between the maximum and minimum values, calculated as: Range = Maximum - Minimum, which indicates the distribution range of the data.
Meaning of data points: Each point represents a data value. Points with the same value are stacked or displayed side by side, and the number of points directly reflects the frequency of that value.

Easy
Dataset: {1, 2, 2, 3, 3, 3, 4}
Draw a dot plot: Mark 1 point at position 1, 2 points at position 2, 3 points at position 3, and 1 point at position 4 on the number line.
Question: What are the minimum, maximum, and range of the dataset?
Answer: Minimum = 1, Maximum = 4, Range = 3.
Medium
Dataset: {5, 5, 6, 6, 6, 7, 8, 8, 9}
After drawing a line plot, answer: What is the most frequent value? What is its frequency?
Answer: The most frequent value is 6, with a frequency of 3.
Hard
The math scores (out of 10) of 10 students in a class are: {7, 8, 8, 9, 9, 9, 10, 10, 10, 10}
After displaying with a dot plot, calculate: The range of the scores; the proportion of students with scores 8 or higher.
Answer: Range = 10 - 7 = 3; 9 students have scores 8 or higher, accounting for 90%.

Step 1: Organize data
Arrange the original data in ascending order to easily identify the minimum, maximum, and repeated values.
Step 2: Draw the graph
Mark all possible values of the data on the number line, and draw the corresponding number of points or lines based on the frequency of each value.
Step 3: Analyze data
- Read the minimum (leftmost point) and maximum (rightmost point) directly from the graph, and calculate the range.
- Observe the density of points to determine the central tendency of the data (e.g., which value occurs most frequently).
- Extract information according to the problem requirements (e.g., the number or proportion of data within a specific range).