Math Problem Statement
The length (in pages) of math research projects is given below. Using this information, calculate the range, variance, and standard deviation.
29, 17, 15, 34, 24, 299, 23, 17, 20
range = variance = standard deviation =
Solution
To calculate the range, variance, and standard deviation of the given data set:
Data set:
29, 17, 15, 34, 24, 299, 23, 17, 20
1. Range
The range is the difference between the maximum and minimum values.
Maximum value = 299
Minimum value = 15
2. Variance
To calculate variance, we first need to find the mean (average) of the dataTo calculate the range, variance, and standard deviation of the given data set:
Data set:
29, 17, 15, 34, 24, 299, 23, 17, 20
1. Range
The range is the difference between the maximum and minimum values.
Maximum value = 299
Minimum value = 15
2. Variance
To calculate variance, we first need to find the mean (average) of the
Now, to calculate the variance, we use the formula:
Let’s compute the squared differences from the mean for each data point:
Now, sum up all the squared differences:
Finally, divide by the number of data points (9):
3. Standard Deviation
The standard deviation is the square root of the variance:
Summary:
Would you like further clarification on any of these steps?
Here are some related questions you might want to explore:
- How does removing the outlier (299) affect the variance and standard deviation?
- What is the difference between population variance and sample variance?
- How would the range change if you added more data points?
- Can you explain why the standard deviation is more robust than the range?
- What is the significance of a high standard deviation in this data set?
Tip: Variance gives a rough idea of how data spreads around the mean, but standard deviation provides a more intuitive sense of this spread because it has the same units as the data.
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Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Measures of Dispersion
Formulas
Range = Maximum value - Minimum value
Variance (σ²) = Σ(Value - Mean)² / N
Standard Deviation (σ) = √Variance
Theorems
No specific theorems involved, general statistical formulas
Suitable Grade Level
Grades 9-12
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