3. Describing Data Numerically
Median
3:15 minutesProblem 3.1.27
Textbook Question
Large Data Sets from Appendix B. In Exercises 25–28, refer to the indicated data set in Appendix B. Use software or a calculator to find the means and medians.
Body Temperatures Refer to Data Set 5 “Body Temperatures” in Appendix B and use the body temperatures for 12:00 AM on day 2. Do the results support or contradict the common belief that the mean body temperature is 98.6oF?
Verified step by step guidance1
Step 1: Extract the relevant data from Data Set 5 in Appendix B, specifically the body temperatures recorded at 12:00 AM on day 2. Ensure you have all the values listed for this specific time and day.
Step 2: Calculate the mean (average) body temperature. To do this, sum all the body temperature values and divide the total by the number of data points. Use the formula: <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Mean</mi><mo>=</mo><mfrac><mrow><mo>∑</mo><mi>x</mi></mrow><mi>n</mi></mfrac></mrow></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> represents each individual temperature and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> is the total number of temperatures.
Step 3: Determine the median body temperature. To find the median, first arrange the data points in ascending order. If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values.
Step 4: Compare the calculated mean and median body temperatures to the commonly believed mean body temperature of 98.6°F. Analyze whether the calculated values support or contradict this belief.
Step 5: Interpret the results. If the mean and median are significantly different from 98.6°F, discuss potential reasons for the discrepancy, such as sample size, measurement errors, or variations in body temperature among individuals.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Mean
The mean, or average, is calculated by summing all values in a data set and dividing by the number of values. It provides a central value that represents the data set as a whole. In the context of body temperatures, calculating the mean helps determine if the average temperature aligns with the commonly accepted value of 98.6°F.
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Median
The median is the middle value in a data set when the values are arranged in ascending order. It is less affected by outliers than the mean, making it a useful measure of central tendency, especially in skewed distributions. Analyzing the median body temperature can provide insights into the distribution of temperatures and whether the mean is a reliable indicator.
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Statistical Significance
Statistical significance assesses whether the results observed in a data set are likely due to chance or represent a true effect. In this context, determining if the mean body temperature significantly differs from 98.6°F involves hypothesis testing, which can help validate or challenge the common belief regarding average body temperature.
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