Answer :
Final answer:
To determine if the statistics of the sample are representative of the current population, we need to calculate the range, variance, and standard deviation of the given data. The range is 1.6 inches, the variance is 0.0314 inches squared, and the standard deviation is 0.177 inches. However, without additional context and comparison to other data sources, we cannot conclude if the statistics are representative of the current population.
Explanation:
To determine if the statistics of the sample are representative of the current population, we need to calculate the range, variance, and standard deviation of the given data. The range is the difference between the largest and smallest foot length values. The variance measures how spread out the data is from the mean, while the standard deviation is the square root of the variance.
- The range = 10.2 - 8.6 = 1.6 inches
- To calculate the variance, first find the mean: (8.6 + 9.5 + 9.6 + 9.2 + 10.1 + 10.1 + 8.9 + 8.7 + 9 + 8.6 + 10.2) / 11 = 9.18
- Next, subtract the mean from each value, square the result, and sum them up: (8.6 - 9.18)^2 + (9.5 - 9.18)^2 + (9.6 - 9.18)^2 + ... + (10.2 - 9.18)^2 = 0.3456
- Finally, divide the sum by the number of data points: 0.3456 / 11 = 0.0314
- The variance = 0.0314 inches squared
- The standard deviation = sqrt(0.0314) = 0.177 inches
Based on this information, we cannot determine if the statistics are representative of the current population without additional context and comparison to other data sources.
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