2. Describing Data with Tables and Graphs
Frequency Distributions
2:40 minutesProblem 2.1.20
Textbook Question
Hershey Kisses Refer to Data Set 38 “Candies” and use the weights (grams) of Hershey’s Kisses. Begin with a lower class limit of 4.300 g and use a class width of 0.100 g. Does this distribution appear to be a normal distribution?
Verified step by step guidance1
Step 1: Organize the data into a frequency distribution table. Start by creating class intervals using the given lower class limit of 4.300 g and the class width of 0.100 g. For example, the first class interval would be 4.300–4.399 g, the second would be 4.400–4.499 g, and so on. Count the number of data points (frequencies) that fall into each class interval.
Step 2: Calculate the midpoints of each class interval. The midpoint of a class interval can be found using the formula: . For example, for the first class interval (4.300–4.399), the midpoint would be (4.300 + 4.399) / 2.
Step 3: Plot a histogram of the frequency distribution. On the x-axis, place the class midpoints, and on the y-axis, place the frequencies. This will help visualize the shape of the distribution.
Step 4: Assess the shape of the histogram. A normal distribution typically appears as a symmetric, bell-shaped curve. Check for symmetry, a single peak, and whether the frequencies taper off evenly on both sides of the peak.
Step 5: Perform a more formal test for normality if needed. This could include calculating the skewness and kurtosis of the data or conducting a statistical test such as the Shapiro-Wilk test or Anderson-Darling test. Compare the results to the criteria for normality to make a final determination.
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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 probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. It is characterized by its bell-shaped curve, defined by its mean and standard deviation. In statistics, many real-world phenomena tend to follow this distribution, making it a fundamental concept in inferential statistics.
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Class Intervals
Class intervals are ranges of values that are used to group data in a frequency distribution. In this context, a lower class limit of 4.300 g and a class width of 0.100 g means that the first class interval would be from 4.300 g to 4.399 g. Properly defining class intervals is crucial for accurately representing data and analyzing its distribution.
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Histogram
A histogram is a graphical representation of the distribution of numerical data, where the data is divided into bins or intervals. Each bin's height represents the frequency of data points within that interval. By constructing a histogram for the weights of Hershey's Kisses, one can visually assess whether the data approximates a normal distribution, looking for the characteristic bell shape.
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