Math Problem Statement
Question content area top Part 1 Find the standard deviation for the group of data items. 9, 5, 9, 5, 9, 5, 9, 5 Question content area bottom Part 1 The standard deviation is enter your response here.
Solution
To find the standard deviation for the given group of data items:
The data set is:
Steps:
- Find the mean (average) of the dataTo find the standard deviation for the given group of data items:
The data set is:
Steps:
-
Find the mean (average) of the
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Calculate the squared deviations from the mean for each data point: Repeating for all values, we get:
-
Find the average of these squared deviations (variance):
-
Take the square root of the variance to find the standard deviation:
Thus, the standard deviation is 2.
Would you like more details on any step? Here are some related questions:
- How do we interpret the standard deviation in this context?
- What happens to the standard deviation if we change one of the 9s to a different number?
- How does standard deviation differ from variance in concept?
- Why do we use the square of deviations when calculating variance?
- What is the standard deviation formula for a sample versus a population?
Tip: Standard deviation measures how spread out the data is relative to the mean.
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Math Problem Analysis
Mathematical Concepts
Statistics
Standard Deviation
Variance
Mean
Formulas
Mean = (Sum of all data points) / (Number of data points)
Variance = Sum of squared deviations from the mean / Number of data points
Standard Deviation = √Variance
Theorems
None (Basic statistical calculation)
Suitable Grade Level
Grades 8-10
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