Textbook Question
True or False: The shape of the distribution shown is best classified as uniform.
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2. Describing Data with Tables and Graphs
Histograms
1:58 minutesProblem 2.2.7
Textbook Question
True or False: The shape of the distribution shown is best classified as skewed left.
Verified step by step guidance1
Step 1: Understand the concept of skewness. A distribution is skewed left (negatively skewed) if the tail on the left side (lower values) is longer or fatter than the right side. Conversely, it is skewed right (positively skewed) if the tail on the right side (higher values) is longer or fatter.
Step 2: Observe the histogram bars. Notice that the tallest bars are on the left side of the graph, and the heights of the bars gradually decrease as you move to the right.
Step 3: Identify the tail of the distribution. Since the bars decrease gradually toward the right, the tail extends to the right side, not the left.
Step 4: Based on the tail direction, conclude the skewness. Because the tail is on the right side, the distribution is skewed right, not skewed left.
Step 5: Therefore, the statement 'The shape of the distribution shown is best classified as skewed left' 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.
Skewness of a Distribution
Skewness describes the asymmetry of a distribution's shape. A distribution is skewed left (negatively skewed) if the tail on the left side is longer or fatter, with most data concentrated on the right. Conversely, skewed right means the tail is longer on the right side.
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Interpreting Histograms
Histograms display data frequency across intervals using bars. Taller bars indicate higher frequencies. By examining the shape and tail lengths of the bars, one can determine the distribution's skewness and overall pattern.
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True or False Questions in Statistics
True or False questions require understanding key definitions and applying them to given data. Correctly classifying distribution shape depends on accurately interpreting the histogram and knowing the criteria for skewness.
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