11. When can the sample standard deviation s be negative? 12. When does the samp
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11. When can the sample standard deviation s be negative? 12. When does the sample standard deviation s equal zero PRACTICING THE TECHNIQUES Find the range of the data in Exercises 13-24. 13. 79,92, 65, 75, 67, 59, 88 14. -50,-51, -45, 50,45, 51 15. 1503, 1642, 1298, 1441, 2000 16. 9.10,9,8,6,5,8,9,6, 10, 8 17. 10, 25, 0, 15, 10 18. 10, 10, 10, 10, 10 19. 18, 15, 20, 20, 17 0. 3,0,5, -3,0,-5 21. 75, 65, 90,80,85,75, 1 22. 120, 155, 95, 155, 133 3. -5,-10,-15,-20 Unless a data set is identified as a population, you can assume that it is a sample CLARIFYING THE CONCEPTS 1. Explain what a deviation is. 2. What is the interpretation of the value of the standard deviation? 3. A small business keeps track of the delivery times for a particular supplier. In this instance, which is better, less variability or more variability? Why? 4. State one benefit and one drawback of using the range as a measure of spread is the range sensitive or robust? Explain what you mean equals what number? median, and mode, then they are identical. 6. The mean of the deviations of any data set always 7. True or false: If two data sets have the same mean. 8. What is one benefit of using the standard deviation instead of the range as a measure of spread? What is one 9. Which measure of spread represents the mean squared 10. True or false: When using the computational formulas 14159, 3.14159, 3.1 data in Exercises 2 alculate the popu ompute the popu 65, 75, 67, 59 51,-45, 50, 1298, 14 lowing: drawback? deviation for the population? calculate the individual deviations viation. for the variance and standard deviation, you do not need toExplanation / Answer
1. As the name suggests, deviation is the difference between the actual observed value and a constant assumed value. The assumed value can be assumed mean, actual mean, median or any other value.
2. Standard deviation measures the spread of the data set from its mean value. A data set with low standard deviation means that the variation means that the variation of the data from its mean value is less and the data is not much spread. While a data set with high standard deviation means that the data values are far away from its mean value.
3. If a small business keeps track of the delivery times for a particular supplier less variability is better because the business might be affected adversely if the supply of raw materials and goods are not delivered in short intervals of time as they might run out of raw materials and goods quickly.
4. Range is the difference between the extreme values of the data set. One advantage of using range is that it is very easy to calculate. Range = maximum value - minimum value. Although, the major drawback of using range is that it is highly affected by outliers and it ignores the intermediate values of the data set.
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