Textbook Question
True or False: The shape of the distribution shown is best classified as skewed left.
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2. Describing Data with Tables and Graphs
Histograms
1:58 minutesProblem 2.2.8
Textbook Question
True or False: The shape of the distribution shown is best classified as uniform.
Verified step by step guidance1
Step 1: Understand the definition of a uniform distribution. A uniform distribution has bars (or frequencies) that are approximately the same height across all intervals, indicating equal frequency or probability for each value range.
Step 2: Observe the histogram provided. Notice that the bars are not all the same height; instead, they rise to a peak in the center and then symmetrically decrease on both sides.
Step 3: Recognize that this shape is characteristic of a symmetric distribution with a single peak, often called a bell-shaped or normal-like distribution, rather than a uniform distribution.
Step 4: Conclude that since the bars are not equal in height and the distribution has a clear center peak, the shape is not uniform.
Step 5: Therefore, the statement 'The shape of the distribution shown is best classified as uniform' is false.
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Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Uniform Distribution
A uniform distribution is one where all outcomes or values have approximately the same frequency or probability. In a histogram, this appears as bars of roughly equal height across the range, indicating no particular value is more common than others.
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Uniform Distribution
Shape of a Distribution
The shape of a distribution describes the overall pattern of data values, such as symmetric, skewed, or uniform. Recognizing the shape helps in understanding the data's behavior and selecting appropriate statistical methods.
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Symmetric Distribution
A symmetric distribution has a balanced shape where the left and right sides mirror each other around a central peak. This often indicates that data values cluster around a central point, unlike a uniform distribution where frequencies are equal.
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