Mathematics
Grade 10
15 min
Interpret line plots
Interpret line plots
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1
Introduction & Learning Objectives
Learning Objectives
Identify the key features of a line plot, including clusters, gaps, and outliers, in the context of geometric data.
Calculate the mean, median, mode, and range for a data set represented by a line plot.
Describe the shape and distribution of data on a line plot, including symmetry and skewness.
Formulate conclusions about a set of two-dimensional figures based on the interpretation of a line plot of their properties.
Compare and contrast two line plots representing different sets of geometric data.
Construct a reasoned argument or proof about geometric properties supported by data from a line plot.
Imagine you have a collection of 50 different triangles. How could you quickly visualize and understand the distribution of their interior angle measures? 🤔 A...
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Key Concepts & Vocabulary
TermDefinitionExample
Line PlotA graph that shows the frequency of data along a number line. An 'X' (or other mark) is placed above each data value on the number line for each time that value occurs.A line plot showing the number of sides of various polygons in a collection. There might be three 'X's above the number 4 (for quadrilaterals) and five 'X's above the number 3 (for triangles).
DistributionThe way in which data points are spread out or clustered together. Key descriptions include symmetric, skewed left, or skewed right.A line plot of the areas of circles with uniformly increasing radii will be skewed to the right, as larger radii produce exponentially larger areas.
ClusterA group of data points that are gathered closely together on a line plot.On a...
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Core Formulas
Mean (Average)
\text{Mean} = \frac{\sum_{i=1}^{n} x_i}{n}
Used to find the mathematical average of the data set. To calculate from a line plot, sum all the values represented by the 'X's and divide by the total number of 'X's (n).
Median
\text{Median} = \text{The middle value of an ordered data set}
Represents the physical center of the data. To find it on a line plot, count the total number of 'X's (n). The median is the value of the ((n+1)/2)-th 'X' when counted from the minimum value.
Range
\text{Range} = \text{Maximum Value} - \text{Minimum Value}
Used to measure the spread or dispersion of the data. It shows the total span covered by the data on the number line.
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Challenging
A line plot shows data for a property of several isosceles triangles. The statistics are: Mean = 62°, Median = 65°, Mode = 70°. The distribution is skewed left. Which property is most likely being measured?
A.The perimeter.
B.The area.
C.The vertex angle.
D.base angle.
Challenging
A line plot displays the ratio of circumference to diameter (Ï€) for 20 circles measured in an experiment. The data is tightly clustered around 3.14, but there is a single outlier at 4.14. A student proposes a proof that this outlier must be due to measurement error. Which feature of the line plot provides the strongest evidence for this claim?
A.The range of the data is approximately 1.0.
B.The data point 4.14 is a significant outlier, far from the dense cluster representing a known mathematical constant.
C.The median of the data is 3.14.
D.The distribution is skewed to the right.
Challenging
A line plot shows the areas of 15 right triangles, all with a hypotenuse of 13 cm. The distribution of the areas is symmetric and unimodal with a peak at 30 cm². What does this distribution shape imply about the leg lengths of the triangles in the sample?
A.Most of the triangles have one very long leg and one very short leg.
B.The leg lengths of the triangles in the sample are all integers.
C.The sample is centered around triangles whose legs are closest to being equal in length.
D.The triangles are all congruent.
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