Find the (a) mean, (b) median, (c) mode, and (d) midrange...

find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. Express answers with the appropriate units of measurement. Then answer the given questions. According to the “freshman 15” legend, college freshmen gain 15 pounds (or 6.8 kilograms) during their freshman year. Listed below are the amounts of weight change (in kilograms) for a simple random sample of freshmen included in a study (“Changes in Body Weight and Fat Mass of Men and Women in the First Year of College: A Study of the 'Freshman 15'” by Hoffman, Policastro, Quick, and Lee, Journal of American College Health, Vol. 55, No. 1). Positive values correspond to students who gained weight and negative values correspond to students who lost weight. Do these values appear to support the legend that college students gain 15 pounds (or 6.8 kilograms) during their freshman year? Why or why not?

find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. Express answers with the appropriate units of measurement. Then answer the given questions.
According to the “freshman 15” legend, college freshmen gain 15 pounds (or 6.8 kilograms) during their freshman year. Listed below
are the amounts of weight change (in kilograms) for a simple random sample of freshmen included in a study (“Changes in Body Weight and Fat Mass
of Men and Women in the First Year of College: A Study of the 'Freshman 15'” by Hoffman, Policastro, Quick, and Lee, Journal of American College
Health, Vol. 55, No. 1). Positive values correspond to students who gained weight and negative values correspond to students who lost weight. Do
these values appear to support the legend that college students gain 15 pounds (or 6.8 kilograms) during their freshman year? Why or why not?

Key Concepts

Mean

The mean is the arithmetic average of a dataset, calculated by summing all the individual values and then dividing by the total number of observations. It provides a measure of the central tendency and is a widely used summary statistic that balances the overall dataset.

Median

The median is the middle value in an ordered dataset, effectively dividing the data into two equal halves. This measure of central tendency is particularly useful because it is less affected by extreme values or outliers compared to the mean.

Mode

The mode refers to the most frequently occurring value in a dataset. It offers insight into the data by indicating which value appears most commonly, and can be particularly useful when the data contains multiple peaks or common responses.

Midrange

The midrange is a measure of central tendency calculated as the average of the smallest and largest values in a dataset. It provides a simple snapshot of the data by equally weighting the two extremes, though it can be sensitive to outliers.

Units of Measurement

Expressing results with the appropriate units of measurement is essential for clarity and proper interpretation. Whether dealing with weight, length, or any other quantifiable metric, the units contextualize the numerical value and ensure the information is accurately communicated.

Inferential Reasoning

Beyond descriptive calculations, comparing the computed statistics to a predetermined claim or legend involves inferential reasoning. This process includes evaluating whether the sample data, through its central tendency measures, supports or contradicts a broader narrative or hypothesis about the population.

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