3. Describing Data Numerically
Mean
2:34 minutesProblem 12.R.4
Textbook Question
Birth Weights The table below lists some of the same data used in the preceding exercise, but the seven days of the week are combined into weekday (Monday, Tuesday, Wednesday, Thursday, Friday) and weekend days (Saturday, Sunday). Also, the birth weights are converted to kilograms. What do you conclude?
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Step 1: Organize the data into two groups: weekday and weekend birth weights for each hospital (Albany, Bellevue, Olean, Strong). This will help in comparing the two groups effectively.
Step 2: Calculate the mean birth weight for each group (weekday and weekend) for each hospital. Use the formula for mean: <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 individual birth weights and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> is the number of observations.
Step 3: Compare the mean birth weights between weekdays and weekends for each hospital. Look for patterns or differences in the averages to identify any trends.
Step 4: Calculate the standard deviation for each group to measure the variability in birth weights. Use the formula for standard deviation: <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>SD</mi><mo>=</mo><msqrt><mfrac><mrow><mo>∑</mo><mo stretchy="false">(</mo><mi>x</mi><mo>-</mo><mi>Mean</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><mi>n</mi></mfrac></msqrt></mrow></math>.
Step 5: Based on the calculated means and standard deviations, interpret the results. Discuss whether there is a significant difference in birth weights between weekdays and weekends, and what this might imply about the data.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Descriptive Statistics
Descriptive statistics summarize and describe the main features of a dataset. In this context, it involves calculating measures such as the mean, median, and range of birth weights for weekdays and weekends across different locations. Understanding these statistics helps in comparing the central tendencies and variations in birth weights between the two time periods.
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Comparative Analysis
Comparative analysis involves evaluating two or more groups to identify differences or similarities. In this case, it requires comparing birth weights recorded on weekdays versus weekends across various locations. This analysis can reveal patterns or trends, such as whether birth weights tend to be higher or lower on specific days.
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Data Interpretation
Data interpretation is the process of making sense of numerical data and drawing conclusions from it. In the context of the provided table, it involves analyzing the birth weight data to determine any significant differences between weekdays and weekends. This skill is crucial for making informed conclusions based on statistical evidence.
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