Problem Analysis and Solution
The provided worksheet focuses on
measures of variability, which are statistical tools used to describe how spread out or dispersed a set of data is. The questions test understanding of concepts such as range, standard deviation, and variance. Let's solve each question step by step.
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Question 1: Range, standard deviation, and variance are 'similar' in that each looks at...
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Range: The difference between the highest and lowest values in a dataset.
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Standard Deviation: A measure of how spread out numbers are from the mean (average).
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Variance: The average of the squared differences from the mean.
All three measures focus on
how spread out the data is. Therefore, the correct answer is:
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Option B: how spread out the data is.
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Question 2: Professor Dublin wants to calculate the 'range' of performance of his students. What must he do?
The
range is calculated as the difference between the highest score and the lowest score in the dataset. To find the range, Professor Dublin must:
1. Identify the highest score.
2. Identify the lowest score.
3. Subtract the lowest score from the highest score.
Thus, the correct answer is:
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Option D: Subtract the lowest score from the highest score.
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Question 3: Professor Dublin wants to calculate the 'standard deviation' of student performance. What must he do?
The
standard deviation is a measure of how much individual scores deviate from the mean (average). To calculate the standard deviation, the following steps are generally followed:
1. Calculate the mean (average) of the scores.
2. For each score, determine how far it is from the mean (this is called the deviation).
3. Square each deviation to eliminate negative values.
4. Calculate the average of these squared deviations (this is the variance).
5. Take the square root of the variance to get the standard deviation.
From the given options, the key step is to identify how far each score is from the average. Therefore, the correct answer is:
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Option C: Identify how far from average each score is.
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Final Answers:
1.
B: how spread out the data is.
2.
D: Subtract the lowest score from the highest score.
3.
C: Identify how far from average each score is.
Boxed Answers:
\[
\boxed{B, D, C}
\]
Parent Tip: Review the logic above to help your child master the concept of measures of variation worksheet.
