Math Problem Statement
Seth asked a random sample of 20 students how much cash they had in their pocket. The following frequency table gives the responses. cash($) freq 0. 1
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2
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4
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11
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1
- 1 Find the standard deviation. Give your answer to at least 2 decimal places
Solution
To calculate the standard deviation of a frequency distribution, we use the formula:
Where:
- = the cash amount (given in the table)
- = frequency (number of students)
- = total number of students
- = mean of the distribution
Let's follow these steps:
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Find the mean :
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Use the mean to calculate the variance:
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Standard deviation is the square root of the variance.
I'll now compute this.The standard deviation of the cash amounts is approximately .
Would you like further details or have any questions about the process?
Here are 5 related questions to expand on this concept:
- How would the standard deviation change if the extreme outlier ($985) was removed?
- Can you explain why the mean and standard deviation are sensitive to outliers?
- What would happen to the standard deviation if all the cash amounts were doubled?
- How is standard deviation different from variance, and why is it often preferred?
- Could you compare this standard deviation with that of a larger sample?
Tip: When calculating the standard deviation, extreme outliers can significantly affect the result, so always check the data for such values!
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Math Problem Analysis
Mathematical Concepts
Statistics
Standard Deviation
Frequency Distribution
Mean
Variance
Formulas
Mean formula: μ = (Σf * x) / N
Variance formula: Variance = Σf * (x - μ)^2 / N
Standard deviation formula: σ = √(Variance)
Theorems
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Suitable Grade Level
Grades 9-12
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