Math Problem Statement
Fi(Xi-μ)2
Solution
It looks like you’re asking for the calculation of , which is part of the variance formula. Let's break this down step by step using the data provided.
Step 1: Recap of Midpoints and Mean
We've already calculated the midpoints () for each score range and the mean () of the distribution:
Step 2: Calculate for Each Midpoint
We need to subtract the mean from each midpoint, square the result, and then multiply by the frequency ():
Score Range | Frequency () | Midpoint () | ||
---|---|---|---|---|
30-39 | 8 | 34.5 | ||
40-49 | 10 | 44.5 | ||
50-59 | 12 | 54.5 | ||
60-69 | 15 | 64.5 | ||
70-79 | 20 | 74.5 | ||
80-89 | 25 | 84.5 | ||
90-99 | 15 | 94.5 |
Step 3: Sum the Values
Now sum up all the values in the column:
Step 4: Calculate the Variance ()
Finally, divide by the total frequency (which is 105) to get the variance:
Step 5: Calculate the Standard Deviation
The standard deviation () is the square root of the variance:
Step 6: Calculate the Coefficient of Variation (CV)
The coefficient of variation is:
Summary for Question 2
- Variance: 328.66
- Standard Deviation: 18.12
- Coefficient of Variation: 25.85%
Do you need any further details or explanations? Here are some related questions:
- How do you interpret the coefficient of variation in a dataset?
- What are the advantages of using standard deviation over variance?
- How does the range compare to the standard deviation as a measure of spread?
- Can the coefficient of variation be used to compare variability between different datasets?
- What is the effect of extreme values on the range and standard deviation?
Tip: Always remember that variance is sensitive to outliers since it squares the deviations from the mean.
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Math Problem Analysis
Mathematical Concepts
Statistics
Variance
Standard Deviation
Coefficient of Variation
Formulas
Variance formula
Standard deviation formula
Coefficient of variation formula
Theorems
-
Suitable Grade Level
Undergraduate
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