Mathematics
Grade 9
15 min
Interpret line plots
Interpret line plots
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1
Introduction & Learning Objectives
Learning Objectives
Calculate the mean, median, mode, and range for a data set represented by a line plot.
Identify clusters, gaps, and potential outliers within a line plot.
Describe the shape of a data distribution (symmetric, skewed left, skewed right) from a line plot.
Determine the total number of data points and their frequency from a line plot.
Formulate a conclusion or inference based on the visual representation of data in a line plot.
Compare and contrast two different data sets presented as line plots.
Ever wondered how a video game developer balances the difficulty of different levels? They analyze data on player completion times, often visualized in plots! 🎮
This tutorial will teach you how to read and interpret line plots, a simple yet powerful tool for visua...
2
Key Concepts & Vocabulary
TermDefinitionExample
Line PlotA graph that shows the frequency of data along a number line. An 'X' or a dot is placed above each data value on the number line for each time the value occurs.A line plot showing the number of pets owned by students might have three 'X's above the number 2, meaning three students own two pets.
FrequencyThe number of times a specific data value appears in a data set.In the data set {2, 3, 3, 3, 5}, the frequency of the value 3 is four.
DistributionThe way in which data is spread out or arranged. Key shapes are symmetric (a bell-like curve), skewed left (tail on the left), and skewed right (tail on the right).A line plot of adult heights is often a symmetric distribution, with most data clustered around the average height.
ClusterA group o...
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Core Formulas
Mean (Average)
\text{Mean} = \frac{\sum_{i=1}^{n} x_i}{n}
To find the mean from a line plot, sum all the data values (multiply each value by its frequency) and divide by the total number of data points (the total count of 'X's).
Median
The middle value of an ordered data set.
List all data values from the line plot in ascending order. The median is the middle value. If there are two middle values, the median is the average of those two.
Mode
The value that appears most frequently.
On a line plot, the mode is the number on the axis with the tallest column of 'X's.
Range
\text{Range} = \text{Maximum Value} - \text{Minimum Value}
Identify the largest and smallest data values that have at least one 'X' above them on the line plot and...
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Challenging
A line plot shows the ages of employees at a tech startup. The distribution is heavily skewed right, with most employees aged 22-30, and a few founders aged 55, 58, and 65. A reporter wants to state the 'typical' age of an employee. Which measure of center should they use and why?
A.The mean, because it includes all data points equally.
B.The range, because it shows the full spread of ages.
C.The median, because it is not strongly affected by the high-aged outliers.
D.The mode, because it is always the most accurate measure.
Challenging
A line plot has the following data for the number of fish in 16 tanks: 10(1), 11(2), 12(3), 13(4), 14(3), 15(2), 16(1). This is a symmetric distribution. If two new tanks are added, each containing 16 fish, how does the median change?
A.The median increases from 13 to 13.5
B.The median stays the same at 13
C.The median increases from 13 to 14
D.The median decreases from 13.5 to 13
Challenging
A line plot shows the number of defects found in 15 batches of a product. The data is: 0(5), 1(4), 2(3), 3(2), 10(1). A data entry error is found: the outlier value of 10 was supposed to be a 1. How does correcting this error affect the mean and median?
A.The mean decreases and the median stays the same.
B.The mean decreases and the median decreases.
C.The mean increases and the median decreases.
D.Both the mean and the median stay the same.
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