2. Describing Data with Tables and Graphs
Histograms
2:28 minutesProblem 2.2.1
Textbook Question
IQ Scores IQ scores of adults are normally distributed. If a large sample of adults is randomly selected and the IQ scores are illustrated in a histogram, what is the shape of that histogram?
Verified step by step guidance1
Understand that IQ scores are normally distributed, which means they follow a bell-shaped curve.
Recall that a normal distribution is symmetric around its mean, with most of the data clustering around the center and tapering off towards the tails.
Visualize the histogram: it will have a peak at the mean IQ score, and the frequencies of scores will decrease symmetrically as you move away from the mean.
Recognize that the histogram will resemble a bell curve, which is characteristic of a normal distribution.
Conclude that the shape of the histogram for IQ scores will be approximately bell-shaped, reflecting the properties of a normal distribution.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Normal Distribution
A normal distribution is a continuous probability distribution characterized by a symmetric, bell-shaped curve. It is defined by its mean and standard deviation, with most data points clustering around the mean. In the context of IQ scores, which are normally distributed, this means that most individuals will have scores near the average, with fewer individuals having extremely high or low scores.
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Histogram
A histogram is a graphical representation of the distribution of numerical data, where data is grouped into bins or intervals. The height of each bar in a histogram represents the frequency of data points within each bin. For normally distributed data, such as IQ scores, the histogram will typically exhibit a bell-shaped curve, reflecting the underlying normal distribution.
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Central Limit Theorem
The Central Limit Theorem states that the distribution of the sample mean will approximate a normal distribution as the sample size becomes large, regardless of the shape of the population distribution. This concept is crucial in understanding why the histogram of a large sample of IQ scores, which are normally distributed, will also display a normal distribution shape, reinforcing the bell curve pattern.
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