Construct a box-plot for the ages of the bachelorettes

Assignment Help Applied Statistics

Reference no: EM131438594

Part A -

Q1. This problem uses data about variability in basketball scores.

The following tables show how many points were scored by the home team and away team for a sample of games during the 2014-2015 season. The scores from away teams are sorted from lowest to highest), but the scores from home teams are not sorted.

Sample of Scores from Away Teams					Sample of Scores from Home Teams
68	76	77	80	80	95	97	74	100	99
81	82	84	85	87	102	78	89	87	79
89	89	91	92	92	86	88	91	105	105
96	97	98	99	100	74	123	96	91	93
101	103	111	112	114	80	97	104	92	111

A. Calculate the values for the minimum, maximum, and range for the data values from away teams.

B. Calculate the values for the minimum, maximum, and range for the scores from home teams. It may be helpful to sort the scores first.

C. Report the values of the first and third quartiles for the scores from away teams. Report the IQR for the scores from away teams.

D. Report the values of the first and third quartiles for the scores from home teams. Report the IQR for the scores from home teams.

E. Calculate the fences for outliers for the scores from away teams. Identify any outliers.

F. Calculate the fences for outliers for the scores from home teams. Identify any outliers.

G. Draw stacked boxplots for the scores from away teams and home teams. Remember to plot any outliers using separate points. Compare the scores based on the graphs. Do the graphs indicate that playing at home can lead to higher scores? Make sure to talk about both center and variability. Refer to the specific graphs to support your conclusion.

Q2. Imagine that an error was made when the data values for typical monthly temperatures in St. Louis were recorded in the table below. The first two digits for the July temperature were reversed. It was supposed to be 79.8 but was written as 97.8.

	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
St. Louis	29.9	33.9	45.1	56.7	66.1	75.4	97.8	77.6	70.2	58.4	46.2	33.9

A. Calculate the range with this new incorrect value and compare it with the original range you calculated in class. How does this error affect the range? Does it increase the range, decrease the range, or leave it unchanged?

B. How does this error affect the IQR? Does it increase the IQR, decrease the IQR, or leave it unchanged? (Note: The IQR is not affected much by outliers and skewing. The range is greatly affected by outliers and skewing.)

C. How does the change affect the box-plot for the data? Explain by sketching the box-plot for the data with the mistake and comparing it to the box-plot for the correct data set that you created in class.

Q3. The following table contains the ages of the 30 women who appeared on the television show The Bachelor in Season 15.

Bachelorette	Age	Bachelorette	Age
Alli	34	Lindsay	25
Ashley H	26	Lisa M	24
Ashley S	26	Lisa P	27
Britnee	25	Madison	25
Britt	25	Marissa	26
Chantal	28	Meghan	30
Cristy	30	Melissa	32
Emily	24	Michelle	30
J	26	Raichel	29
Jackie	27	Rebecca	30
Jill	28	Renee	28
Keltie	28	Sarah L	25
Kimberly	27	Sarah P	27
Lacey	27	Shawntel	25
Lauren	26	Stacey	26

A. Construct a dotplot or histogram for the ages of the bachelorettes. Describe important features of the graph.

B. Report the values in the five-number summary for the ages of the bachelorettes.

C. Construct a box-plot for the ages of the bachelorettes. Compare the box-plot you constructed in this question to the graph you constructed in Question 3A. Which do you think better represents the distribution of the ages of the bachelorettes? Explain your reasoning.

D. Think about what "quartiles" means. The quartiles divide the data set into four equal parts. What proportion of the bachelorettes were older than 26.5?

E. Looking at the box-plot, can you tell if the distribution of ages is skewed? If it is skewed, is it skewed left or right?

F. Based on what you see in the box-plot of bachelorette ages, do you think the mean or median age is likely to be larger? Give a reason for your answer.

G. Calculate the mean age for the bachelorettes. Compare it to the median. Was your answer to Question F correct?

H. What range of values represents the middle 50% of the values?

Part B -

1. Here are the names and ages of the 30 women who appeared on the television show. The Bachelor in Season 15.

Bachelorette	Age	Bachelorette	Age
Alli	34	Lindsay	25
Ashley H	26	Lisa M	24
Ashley S	26	Lisa P	27
Britnee	25	Madison	25
Britt	25	Marissa	26
Chantal	28	Meghan	30
Cristy	30	Melissa	32
Emily	24	Michelle	30
J	26	Raichel	29
Jackie	27	Rebecca	30
Jill	28	Renee	28
Keltie	28	Sarah L	25
Kimberly	27	Sarah P	27
Lacey	27	Shawntel	25
Lauren	26	Stacey	26

The ages are summarized in the dot-plot below.

The mean of these ages is 26.9 years. Compute the standard deviation for the ages of the women on the show. Include units with your answer. Explain what the standard deviation means in the context of their ages.

Q2. We examined the weight gains (in grams) over a one-month period for two samples of laboratory rats. One sample contained six adolescent rats that were given a high daily dose of a stimulant drug. This sample was called the Treatment group. The sample of six normal adolescent laboratory rats was the Control group. This group received no treatment.

Here are the weight gains for the two groups:

Control Group	169	154	179	202	197	175
Treatment Group	137	158	153	147	168	147

These values are summarized in the dot-plots below.

A. Use technology to compute the standard deviations for the weight gains in each group. Be sure to include the units.

B. Write a brief comparison of the standard deviations for the weight gains of the two groups. When making your comparison, think about differences, or variability, between the groups. Also think about whether the standard deviations show that the variability in the distributions is substantially different or not. Explain your reasoning.

Reference no: EM131438594

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