A simple random sample of 85 is drawn from a normally distributed population, and the mean is found to be 146, with a standard d
2 answers:
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Answer:
--- Standard deviation
Step-by-step explanation:
Given
See attachment for graph
Solving (a): Explain how the standard deviation is calculated.
<u>Start by calculating the mean</u>
To do this, we divide the sum of the products of grade and number of students by the total number of students;
i.e.
So, we have:
Next, calculate the variance using the following formula:
i.e subtract the mean from each dataset; take the squares; add up the squares; then divide the sum by the number of dataset
So, we have:
Lastly, take the square root of the variance to get the standard deviation
--- approximated
<em>Hence, the standard deviation is approximately 11.28</em>
Considering the calculated mean (i.e. 82.76), the standard deviation (i.e. 11.28) is small and this means that the grade of the students are close to the average grade.
