Homework Example Chapter 1 Similar to Problem #14

Transcription

1 Chapter 1 Similar to Problem #14 Given a sample of n = 129 observations of shower-flow-rate, do this: a.) Construct a stem-and-leaf display of the data. b.) What is a typical, or representative flow rate? c.) Does the distribution appear to be highly concentrated or spread out? d.) Is the distribution symmetric? If not, how would you describe the departure from symmetry? e.) Would you describe an observation as being far from the rest of the data (an outlier)? K.Paulk - C01_all 39

2 Chapter 1 Similar to Problem #14 (cont.) a.) Construct a stem-and-leaf display of the data. Minitab Notes: Put data into a column Graph, Stem-and-leaf Select your column OK Minitab Output: 3 columns 1 st column is a count Row with median has parens Stem-and-Leaf Display: Shower Flow Rate Stem-and-leaf of Shower Flow Rate N = 129 Leaf Unit = (17) and 2.3 K.Paulk - C01_all 40

3 Chapter 1 Similar to Problem #14 (cont.) b.) What is a typical, or representative flow rate? Minitab Notes: Stats, Basic Stats Display Descriptive Statistics Descriptive Statistics: Shower Flow Rate Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Shower Flow Rate Variable Maximum Shower Flow Rate K.Paulk - C01_all 41

4 Chapter 1 Similar to Problem #14 (cont.) c.) Does the distribution appear to be highly concentrated or spread out???? d.) Is the distribution symmetric? If not, how would you describe the departure from symmetry???? e.) Would you describe an observation as being far from the rest of the data (an outlier)???? K.Paulk - C01_all 42

5 Chapter 1 Similar to Problem #14 (cont.) c.) Does the distribution appear to be highly concentrated or spread out? Concentrated. d.) Is the distribution symmetric? If not, how would you describe the departure from symmetry? Not Symmetric. Skewed right. e.) Would you describe an observation as being far from the rest of the data (an outlier)? The max value is an outlier K.Paulk - C01_all 43

6 Chapter 1 Similar to Problem #20 Given n = 47 observations of street length within a subdivision. (b.) Construct a histogram using class boundaries 0, 1000, 2000, 3000, 4000, 5000, What proportion of subdivisions have total length less than 2000? Between 2000 and 4000? How would you describe the shape of the histogram? K.Paulk - C01_all 44

7 Chapter 1 Similar to Problem #20 (cont.) Minitab Notes: Enter data Graph Histogram, Simple Select data OK Change Binning Click Graph Edit Bars Binning Midpoints 500, 1500, 2500, 3500, 4500, 5500 K.Paulk - C01_all 45

8 Chapter 1 Similar to Problem #20 (cont.) With Midpoints: 500, 1500, 2500, 3500, 4500, 5500 K.Paulk - C01_all 46

9 Chapter 1 Similar to Problem #20 (cont.) Change Binning Click Graph Edit Bars Binning Cutpoints 0, 1000, 2000, 3000, 4000, 5000, 6000 K.Paulk - C01_all 47

10 Chapter 1 Similar to Problem #20 (Extra) What proportion of subdivisions have total length less than 2000? (Hints: Recall n = 47. Use the histogram.) Proportion =??? Between 2000 and 4000? Proportion =??? How would you describe the shape of the histogram? Skewed K.Paulk - C01_all 48

11 Chapter 1 Similar to Problem #20 (Extra) What proportion of subdivisions have total length less than 2000? (Hints: Recall n = 47. Use the histogram.) Proportion = = =.48 Between 2000 and 4000? Proportion = = =.36 How would you describe the shape of the histogram? Skewed Right. K.Paulk - C01_all 49

12 Chapter 1 Similar to Problem #36 Given a sample of n = 26 escape times in seconds. 26 values a.) Construct a stem-and-leaf display. How does it suggest that the sample mean and median will compare? b.) Calculate the values of the sample mean and median. [ Hint: x i = ] c.) By how much could the largest time (424) be increased without affecting the value of the sample median? By how much could it be decreased? d.) What are the values of x and x when observations are reexpressed in minutes? K.Paulk - C01_all 50

13 Chapter 1 Similar to Problem #36 (cont.) (a.) Construct a Stem-and-Leaf diagram. How will mean and median compare? Minitab Notes: Input data Graph Stem-and-Leaf Select data OK Symmetric so mean ~ median Stem-and-Leaf Display: Escape Time (sec) Stem-and-leaf of Escape Time (sec) N = 26 Leaf Unit = K.Paulk - C01_all 51

14 Chapter 1 Similar to Problem #36 (cont.) b.) Calculate the values of the sample mean and median. [ Hint: x i = ] The hint is helpful in calculating the mean, but to find the median, we would have to put all observations in order then find the middle value. Use Minitab instead! Minitab: Calc, Stats, Descriptive Stats Descriptive Statistics: Escape Time (sec) Variable N N* Mean SE Mean StDev Minimum Q1 Median Escape Time K.Paulk - C01_all 52

15 Chapter 1 Similar to Problem #36 (cont.) c.) By how much could the largest time (424) be increased without affecting the value of the sample median? By how much could it be decreased? The largest value could be increased by??? The largest value could be decreased to??? K.Paulk - C01_all 53

16 Chapter 1 Similar to Problem #36 (cont.) c.) By how much could the largest time (424) be increased without affecting the value of the sample median? By how much could it be decreased? The largest value could be increased by any amount and not affect the median. The largest value could be decreased to any value that is greater than the median (369.5). In other words, you can decrease max value to 370 which is a decrease of 54 ( = 54). K.Paulk - C01_all 54

17 Chapter 1 Similar to Problem #36 (cont.) d.) What are the values of x and x when observations are reexpressed in minutes? Minitab: Calc, Stats, Descriptive Stats Mean = sec. Median = sec. Just convert the seconds to minutes by dividing by 60. Mean = sec. Median = sec. 1 min. 60 sec. 1 min. 60 sec. =??? =??? K.Paulk - C01_all 55

18 Chapter 1 Similar to Problem #36 (cont.) d.) What are the values of x and x when observations are reexpressed in minutes? Minitab: Calc, Stats, Descriptive Stats Mean = sec. Median = sec. Just convert the seconds to minutes by dividing by 60. Mean = sec. Median = sec. 1 min. 60 sec. 1 min. 60 sec. = 6.18 min. = 6.16 min. K.Paulk - C01_all 56

19 Chapter 1 Similar to Problem #60 Burst strength for two types of canisters Test and Canister Given two sets of data. n 1 = 11 and n 2 = data values and 12 data values a.) Construct a comparative boxplot and comment. K.Paulk - C01_all 57

20 Chapter 1 Similar to Problem #60 (cont.) Minitab Notes: Graph Boxplot Multiple Y s Select Data OK K.Paulk - C01_all 58

21 Chapter 1 Similar to Problem #60 (cont.) Minitab Notes: Graph Boxplot Multiple Y s Select Data Scale Transpose X & Y OK Observations: Higher values for Test More variation for Test 2 Outliers for Canister K.Paulk - C01_all 59