Scenario: A local community centre runs a health awareness campaign about hydration. Nine participants recorded how many cups of water they drank per day during a typical weekday. The results (in cups) are: 5, 6, 7, 6, 8, 10, 7, 9, 6Task: a) Calculate the mean, variance, and standard deviation (to two decimals) for this sample. Include all steps, including the sum of squared deviations: ∑(x − x̄)². b) Interpret the results in the context of daily hydration habits. What do the measures of central tendency and spread tell you about how the group behaves? Clearly explain what the numerical value of the standard deviation means in this context, and suggest a realistic goal based on your interpretation. c) Another group recorded an average of 7.00 cups per day with a standard deviation of 0.71 cups.Compare the two groups’ data and explain which group is more consistent. Then, describe how this finding could help a community leader or coach make a realistic recommendation to participants.

Question

BlackTom AI · Accepted Answer

{"reasoning": "a) **Calculations:**\n\nGiven data: 5, 6, 7, 6, 8, 10, 7, 9, 6\n\n1. **Mean (x̄):**\n   $$ x̄ = \frac{5 + 6 + 7 + 6 + 8 + 10 + 7 + 9 + 6}{9} = \frac{64}{9} \approx 7.11 \text{ cups} $$\n\n2. **Sum of Squared Deviations:**\n   $$ \sum (x - x̄)^2 = (5-7.11)^2 + (6-7.11)^2 + (7-7.11)^2 + (6-7.11)^2 + (8-7.11)^2 + (10-7.11)^2 + (7-7.11)^2 + (9-7.11)^2 + (6-7.11)^2 $$\n   $$ = 4.45 + 1.23 + 0.01 + 1.23 + 0.79 + 8.37 + 0.01 + 3.57 + 1.23 = 20.89 $$\n\n3. **Sample Variance (s²):**\n   $$ s^2 = \frac{\sum (x - x̄)^2}{n-1} = \frac{20.89}{8} \approx 2.61 \text{ cups}^2 $$\n\n4. **Standard Deviation (s):**\n   $$ s = \sqrt{s^2} = \sqrt{2.61} \approx 1.62 \text{ cups} $$\n\n**Summary:**\n- Mean: 7.11 cups\n- Variance: 2.61 cups²\n- Standard Deviation: 1.62 cups\n\nb) **Interpretation:**\n\nThe mean daily water intake of 7.11 cups suggests that, on average, participants are consuming a reasonable amount of water. The standard deviation of 1.62 cups indicates variability in daily intake, with some participants drinking significantly more or less than the average. This variability suggests that while some

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