2. Describing Data with Tables and Graphs
Frequency Distributions
3:20 minutesProblem 2.1.19
Textbook Question
Freshman 15 Refer to Data Set 13 “Freshman 15” and use the second column, which lists weights (kg) in September of college freshmen. Begin with a lower class limit of 40 kg and use a class width of 10 kg. Does the distribution appear to be a normal distribution?
Verified step by step guidance1
Step 1: Organize the data into a frequency distribution table. Start by identifying the lower class limit as 40 kg and use a class width of 10 kg. Create intervals such as 40-49, 50-59, 60-69, and so on, until all data points are covered.
Step 2: Count the number of data points (weights) that fall into each class interval. Record these frequencies in the table.
Step 3: Calculate the midpoint for each class interval. The midpoint is found using the formula: , where is the lower class limit and is the upper class limit.
Step 4: Plot a histogram using the class intervals on the x-axis and the frequencies on the y-axis. Observe the shape of the histogram to determine if it resembles a bell curve, which is characteristic of a normal distribution.
Step 5: Perform additional checks for normality, such as calculating the mean and standard deviation of the data, and comparing the frequencies to the expected frequencies of a normal distribution using a normal probability plot or statistical tests like the Shapiro-Wilk test.
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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, where the mean, median, and mode are all equal. Understanding this concept is crucial for determining if the weights of freshmen follow this pattern.
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Class Intervals
Class intervals are ranges of values that are grouped together for the purpose of frequency distribution. In this case, a lower class limit of 40 kg and a class width of 10 kg means the intervals will be 40-49 kg, 50-59 kg, and so on. Analyzing data using class intervals helps in visualizing the distribution of weights and identifying patterns.
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Descriptive Statistics
Descriptive statistics summarize and describe the main features of a dataset, including measures of central tendency (mean, median, mode) and measures of variability (range, variance, standard deviation). These statistics provide insights into the distribution of weights and help assess whether the data aligns with the characteristics of a normal distribution.
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