Math Problem Statement
A researcher has obtained the number of hours worked per week during the summer for a sample of fifteen students. 38 23 33 28 18 38 28 18 38 8 28 18 8 3 18 Using this data set, compute the following. (a) median in hours per week hr/week (b) mean in hours per week hr/week (c) mode in hours per week hr/week (d) 40th percentile in hours per week hr/week (e) range in hours per week hr/week (f) sample variance (Round your answer to two decimal places.) (g) standard deviation in hours per week (Round your answer to two decimal places.) hr/week
Solution
Here are the results based on the given dataHere are the results based on the given
(a) Median: 23.0 hr/week
(b) Mean: 23.0 hr/week
(c) Mode: 18 hr/week
(d) 40th Percentile: 18.0 hr/week
(e) Range: 35 hr/week
(f) Sample Variance: 128.57 hr² (rounded to two decimal places)
(g) Standard Deviation: 11.34 hr/week (rounded to two decimal places)
Would you like more details or have any questions?
Here are some related questions to deepen your understanding:
- What does the mode tell us about the distribution of hours worked?
- How would you interpret the 40th percentile in this context?
- What is the significance of the standard deviation in understanding the variability of the data?
- How does the range help in assessing the spread of the data?
- Why is sample variance important in statistical analysis?
Tip: When calculating variance and standard deviation, always use the correct degrees of freedom (ddof=1 for sample variance).
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Math Problem Analysis
Mathematical Concepts
Statistics
Descriptive Statistics
Measures of Central Tendency
Measures of Spread
Formulas
Mean: (Σx) / n
Median: Arrange data in order, middle value
Mode: Most frequent value
Percentile: Pth Percentile = ((n+1) * P) / 100
Range: Max - Min
Sample Variance: Σ(x - x̄)² / (n - 1)
Standard Deviation: sqrt(variance)
Theorems
Empirical Rule (for standard deviation)
Percentile Calculation Formula
Suitable Grade Level
Grades 9-12
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