Ch. 2 - Exploring Data with Tables and Graphs

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 2 - Exploring Data with Tables and Graphs

Problem 2.1.19

Chapter 2, Problem 2.1.19

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 guidance

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:

m = \frac{l + u}{2}

, where

l

is the lower class limit and

u

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.

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.

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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