A data set is formed by recording the sums in 400 rolls of a pair of a
ambiguit
Answered question
2021-11-27
Answer & Explanation
Witheyesse47
Beginner2021-11-28Added 14 answers
Step 1
Standard deviation:
The standard deviation indicates by how much each observation differs from a central point represented by the mean. Standard deviation is the square root of the variance. In general, the variance increases with the increase in the distances between the individual observations and the mean of the data set.
The general formula for standard deviation is,
Standard deviation
Step 2
Here, first data set is formed by recording the sum in 400 rolls of a pair of dice. Second data set is obtained by recording the result of 600 draws of a ball from a box containing 11 balls numbered 2 through 12. In both data sets, the outcomes are the numbers from 2 to 12. The sample sizes for the first and second data sets are 400 and 600, respectively.
It is known that, as the sample size increases the standard deviation of the sample mean decreases. In this situation sample size for the second data set is larger compared to the first data set. Therefore, it is expect that second data set have a smaller standard deviation.
Step 3
Answer:
Second data set have a smaller standard deviation.
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