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Week 1 Assignment: Skewness and Standard Deviation
A food processing plant fills snack-sized bags of crackers. The mean number of crackers in each bag is 22 and the standard deviation is 2. The factory supervisor selects one bag that contains 24 crackers. Which of the following statements is true? Perfect. Your hard work is paying off 🐀 The number of crackers in the supervisor’s bag is 2 standard deviations to the right of the mean. The number of crackers in the supervisor’s bag is 2 standard deviations to the left of the mean. The number of crackers in the supervisor’s bag is 1 standard deviation to the right of the mean. The number of crackers in the supervisor’s bag is 1 standard deviation to the left of the mean.
Answer Explanation
Correct answer: The number of crackers in the supervisor’s bag is 1 standard deviation to the right of the mean.
Question
The following data set represents the ages of all 6 of Nancy's grandchildren. 11 , 8 , 5 , 6 , 3 , 9 To determine the "spread" of the data, would you employ calculations for the sample standard deviation, or population standard deviation for this data set?
That's incorrect - mistakes are part of learning. Keep trying! Use calculations for sample standard deviation Use calculations for population standard deviation
Answer Explanation
Correct answer: Use calculations for population standard deviation To determine if sample standard deviation or population standard deviation should be used, determine if the data set represents data values collected from the entire population, or from a subset of the population. If the data values represent data collected from a subset of the population, then the sample standard deviation should be used. If the data values represent data collected from the entire population of interest, then the population standard deviation should be used. In this case, the population standard deviation should be used because the data set represents all of, that is the total population of, Nancy's grandchildren Back to Top Activity 3 of 83
Learning Objective
Compute variance and standard deviation
Work Time
24s Monday, Mar 1, 2021 at 4:12pm EDT
Question
The following data set represents the ages of all 6 of Nancy's grandchildren.
So the variance is 7.
Question
The following data set represents the ages of all 6 of Nancy's grandchildren. 11 , 8 , 5 , 6 , 3 , 9 Given that the variance of this data set is 7 , what is the standard deviation of their ages? Round the final answer to one decimal place. Answer 1: Keep trying - mistakes can help us grow. std= 4$$ std= 4 - incorrect Answer 2: Keep trying - mistakes can help us grow. std= 4$$ std= 4 - incorrect
Answer Explanation
Correct answers: std= 2 point 6 $\text{std=}2.6$
Remember that the standard deviation is the square root of the variance. Since we just found that the variance is 7 , we find that the standard deviation is 7 ‾√≈2.6457..., or 2.6 to the nearest tenth.
Question
Which of the following frequency tables show a skewed data set? Select all answers that apply. That's incorrect - mistakes are part of learning. Keep trying! Value Frequency 0 2 1 11 2 30 3 22 4 15 5 12 6 6 7 1 8 1 Value Frequency 4 1 5 2 6 3
Answer Explanation
Correct answer: Value Frequency 0 2 1 11 2 30 3 22 4 15 5 12 6 6
Value Frequency 13 1 14 6 15 9 16 15 17 27 18 28 19 10 20 4 Remember that data are left skewed if there is a main concentration of large values with several much smaller values. Similarly, right skewed data have a main concentration of small values with several much larger values. We can see that the following is left skewed because of the concentration of large values with many smaller values: Value Frequency 13 1 14 6 15 9 16 15 17 27 18 28 19 10 20 4 And the following is right skewed because of its concentration of small values with many larger values: Value Frequency 0 2 1 11 2 30
response - incorrect Answer 2: That's incorrect - mistakes are part of learning. Keep trying! Illinois: z is equal to $z=$ 0 point 6 2 5$$ 0 point 6 2 5 - incorrect Florida: z is equal to $z=$ 0 point 7 5$$ 0 point 7 5 - incorrect response - incorrect
Answer Explanation
Illinois: z is equal to $z=$ 1 $$ 1 - no response given Florida: z is equal to $z=$ 2 $$ 2 - no response given Correct answers: 1 negative 0 point 6 2 5 $-0.625$ 2 negative 0 point 7 5 $-0.75$
The mean monthly electric bill in Illinois is $ 85 , with a standard deviation of $3.20. The z - score corresponding to Stephan's IL electric bill of $ 83 is z = x − μσ = 83 −853.2=−0. The mean monthly electric bill in Florida is $ 105 , with a standard deviation of $4.00. The z - score corresponding to Stephan's FL electric bill of $ 102 is z = x − μσ = 102 −1054.00=−0.
Question
Based on the z -scores calculated above for Stephan's electric bills in IL and FL, in which state is his electric bill higher, when compared to their respective distributions? Well done! You got it right. Illinois Florida Stephan's electric bills in both states are comparable. There is not enough information for a comparison.
Answer Explanation
Correct answer: Illinois
A histogram has a horizontal axis from 0.00 to 20.00 in increments of 2.00 and a vertical axis from 0 to 40 in increments of 10. The histogram has vertical bars of width 2.00 starting at the horizontal axis value 4.00. The approximate heights of the bars are as follows, where the left horizontal axis label is listed first and the approximate height is listed second: 4.00, 19; 6.00, 31; 8.00, 36; 10.00, 31; 12.00, 26.
A histogram has a horizontal axis from 0.00 to 20.00 in increments of 2.00 and a vertical axis from 0 to 40 in increments of 10. The histogram has vertical bars of width 2.00 starting at the horizontal axis value 0.00. The approximate heights of the bars are as follows, where the left horizontal axis label is listed first and the approximate height is listed second: 0.00, 3; 2.00, 14; 4.00, 6; 6.00, 17; 8.00, 37; 10.00, 27; 12.00, 21; 14.00, 11; 16.00, 18; 18.00, 17.
A histogram has a horizontal axis from 0.00 to 20.00 in increments of 2.00 and a vertical axis from 0 to 40 in increments of 10. The histogram has vertical bars of width 2.00 starting at the horizontal axis value 4.00. The approximate heights of the bars are as follows, where the left horizontal axis label is listed first and the approximate height is listed second: 4.00, 19; 6.00, 31; 8.00, 36; 10.00, 31; 12.00, 26. Remember that the standard deviation is a measure of how spread out the data is. If the values are concentrated around the mean, then a data set has a lower standard deviation. A histogram with a taller hill indicates higher frequencies of the same values, and has a lower standard deviation than a histogram with a shorter hill and a wider range of values. The following data set represents the ages of all 6 of Nancy's grandchildren. 11,8,5,6,3, Find the variance of their ages. If necessary, round the final answer to one decimal place. Answer 1:
Keep trying - mistakes can help us grow. variance= 4$$ variance= 4 - incorrect Answer 2: That's incorrect - mistakes are part of learning. Keep trying! variance= 4$$ variance= 4 - incorrect
Answer Explanation
Correct answers: variance= 7 $\text{variance=}7$ First, we find that the mean is 11+8+5+6+3+96=426= Now, we need to take the deviations from the mean and square them: Value1185639Deviation4.01.0−2.0−1.0−4.02.0Deviation 2 16.01.04.01.016.
Since the total population of grandchildren is included, we find the population variance. Add up the squared deviations and divide by the number of data values: 16+1+4+1+16+46= So the variance is 7. The following data set represents the ages of all 6 of Nancy's grandchildren. 11,8,5,6,3,
Compute the z -scores for Stephan's IL and FL electric bills. Round to three decimal places if necessary. Answer 1: That's not right - let's review the answer. Illinois: z is equal to $z=$ 0 point 6 2 5$$ 0 point 6 2 5 - incorrect Florida: z is equal to $z=$ 0 point 7 5$$ 0 point 7 5 - incorrect response - incorrect Answer 2: Not quite - review the answer explanation to help get the next one. Illinois: z is equal to $z=$ 0 point 6 2 5$$ 0 point 6 2 5 - incorrect Florida: z is equal to $z=$ 0 point 7 5$$ 0 point 7 5 - incorrect response - incorrect
Answer Explanation
Illinois: z is equal to $z=$ 1 $$ 1 - no response given Florida: z is equal to $z=$ 2 $$ 2 - no response given Correct answers: 1 negative 0 point 6 2 5 $-0.625$ 2 negative 0 point 7 5 $-0.75$ The mean monthly electric bill in Illinois is $ 85 , with a standard deviation of $3.20. The z - score corresponding to Stephan's IL electric bill of $ 83 is z = x − μσ = 83 −853.2=−0. The mean monthly electric bill in Florida is $ 105 , with a standard deviation of $4.00. The z - score corresponding to Stephan's FL electric bill of $ 102 is z = x − μσ = 102 −1054.00=−0.
Question
If the median of a data set is 13 and the mean is 23 , which of the following is most likely? Not quite - review the answer explanation to help get the next one. The data are skewed to the left.
