QQuestionStatistics
QuestionStatistics
Calculate the standard deviation for the given data set:
10, 15, 18, 22, 36, 52
12 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1:I'll solve this step-by-step using the standard deviation formula:
Step 2:: Calculate the Mean (Average)
\bar{x} = \frac{10 + 15 + 18 + 22 + 36 + 52}{6} = \frac{153}{6} = 25.5
First, I'll find the arithmetic mean by summing all values and dividing by the number of data points.
Step 3:: Calculate the Variance
- $$(52 - 25.5)^{2} = (26.5)^{2} = 702.25
Subtract the mean from each data point and square the differences:
Step 4:: Calculate the Variance
s^{2} = \frac{240.25 + 110.25 + 56.25 + 12.25 + 110.25 + 702.25}{5} = \frac{1231.5}{5} = 246.3
Sum the squared differences and divide by (n- 1):
Step 5:: Calculate Standard Deviation
s = \sqrt{246.3} = 15.7
Take the square root of the variance:
Final Answer
The standard deviation is 15.7.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students