Mathematics
Grade 10
15 min
Create and interpret line plots with fractions
Create and interpret line plots with fractions
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1
Introduction & Learning Objectives
Learning Objectives
Construct a line plot to display a data set of fractional measurements derived from geometric figures.
Calculate and interpret measures of central tendency (mean, median, mode) for a data set represented on a line plot with fractions.
Calculate and interpret measures of spread (range, interquartile range) for a fractional data set on a line plot.
Analyze the shape and distribution (skewness, symmetry, outliers) of a data set from a line plot with fractions.
Solve multi-step problems by redistributing data points on a line plot to achieve a specific statistical measure.
Formulate a logical argument or justification based on the interpretation of a line plot with fractional data, connecting it to a geometric context.
Ever wondered how engineers ensure thous...
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Key Concepts & Vocabulary
TermDefinitionExample
Line PlotA graphical display of data on a number line, where an 'X' or dot is placed above a value for each occurrence of that value in the data set.A line plot showing the lengths of bolts might have three 'X's above the 2 1/4 inch mark, indicating three bolts of that length.
Measures of Central TendencyStatistical values that describe the center or typical value of a data set. The main measures are mean, median, and mode.For the data set {1/2, 1/2, 3/4, 1}, the mean is 11/16, the median is 5/8, and the mode is 1/2.
Measures of Spread (Variability)Statistical values that describe how spread out the data points are. Common measures include the range and interquartile range (IQR).For the data set {1/4, 1/2, 1, 1 1/4}, the range is (1 1/4) - (1/4) =...
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Core Formulas
Mean (Average)
\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}
To find the mean, sum all the data values (x_i) and divide by the total number of data points (n). This is useful for finding the 'balance point' of the data.
Range
Range = Maximum Value - Minimum Value
The simplest measure of spread. It shows the total span of the data but can be heavily influenced by outliers.
Interquartile Range (IQR)
IQR = Q3 - Q1
A robust measure of spread that describes the range of the middle 50% of the data. Q1 is the median of the lower half of the data, and Q3 is the median of the upper half.
4 more steps in this tutorial
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Challenging
A line plot shows the side lengths of 4 regular octagons: 6 1/2, 6 3/4, 7, 7 1/4 inches. The manufacturer wants to add a 5th octagon so that the new mean side length is exactly 7 inches. What must be the side length of the 5th octagon?
A.7 1/2 inches
B.7 1/2 inches
C.8 inches
D.8 1/2 inches
Challenging
A line plot shows the diameters of circular gears produced by a machine. The target diameter is 10 1/2 cm. The plot shows a symmetric distribution centered at 10 1/2 cm, but with a very large range (from 9 cm to 12 cm). Which argument is the most logical conclusion about the manufacturing process?
A.The process is biased, consistently producing gears that are too large.
B.The process is accurate on average, but it is not precise.
C.The process is precise but not accurate, as the values are close together but off-target.
D.The process is both accurate and precise.
Easy
According to the tutorial, what is the primary purpose of using an 'X' or a dot above a number on a line plot's axis?
A.To indicate the frequency of each data value.
B.To calculate the mean of the data set.
C.To represent the range of the data.
D.To mark the position of the median.
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