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|Prompt=A researcher is studying the optimal dose of omeprazole required for relief of gastroesophageal reflux disease symptoms (GERD). For his experiment, he enrolled 240 patients known to have GERD who complain of similar symptoms. The patients first receive a dose of 10 mg of omeprazole by mouth, and incremental increase by 5 mg is added for patients who do not report symptomatic relief. The optimal dose of omepraozale is documented as the minimum dose at which the subjects report relief.  Following data collection, the researcher demonstrates his findings on the graph shown below.  Based on his findings, which of the following statements regarding the mean, median, and mode is correct?
|Prompt=A researcher is studying the optimal dose of omeprazole required for relief of gastroesophageal reflux disease symptoms (GERD). For his experiment, he enrolled 240 patients known to have GERD who complain of similar symptoms. The patients first receive a dose of 10 mg of omeprazole by mouth, and incremental increase by 5 mg is added for patients who do not report symptomatic relief. The optimal dose of omepraozale is documented as the minimum dose at which the subjects report relief.  Following data collection, the researcher demonstrates his findings on the graph shown below.  Based on his findings, which of the following statements regarding the mean, median, and mode is correct?


[[WBR:Graph_GERD_Experiment.png|400px]]
[[WBR:Graph_Graph_Omeprazole.png|400px]]
|Explanation=Based on the graph above, the distribution of the researcher's findings show a negatively skewed graph because the tail of the graph is towards the negative side.  In such graphs, the relationship of the mean, median, and mode are always as follows: mode > median > mean.
|Explanation=Based on the graph above, the distribution of the researcher's findings show a positively skewed graph because the tail of the graph is towards the positive side.  In such graphs, the relationship of the mean, median, and mode are always as follows: mean > median > mode.


In contrast, a positively skewed graph, where the tail is towards the more positive values, the relationship is always as follows: mean > median > mode. Notably, in both positively and negatively skewed graphs, the median is always in the middle.
In contrast, a negatively skewed graph, where the tail is towards the more negative values, the relationship is always as follows: mode > median > mean. Notably, in both positively and negatively skewed graphs, the median is always in the middle.


Graphs with normal distribution typically have mean = median = mode.  
Graphs with normal distribution typically have mean = median = mode.  


Educational Objective: Negatively skewed graphs, with the tail towards the negative side, always have mode > median > mean.
Educational Objective: Positively skewed graphs, with the tail towards the more positive side, always have mean > median > mode.
|AnswerA=Median > Mode > Mean
|AnswerA=Median > Mode > Mean
|AnswerAExp=This is not the relationship in negatively skewed graphs.
|AnswerAExp=This is not the relationship in positively skewed graphs.
|AnswerB=Mode > Median > Mean
|AnswerB=Mode > Median > Mean
|AnswerBExp=This is the correct relationship between mean, median, and mode in negatively skewed graphs.
|AnswerBExp=This would be a correct answer in negatively skewed graphs.
|AnswerC=Mean > Median > Mode
|AnswerC=Mean > Median > Mode
|AnswerCExp=This option would be correct in positively skewed graphs, where the tail is on the positive side of the graph.
|AnswerCExp=This is the correct relationship between mean, median, and mode in positively skewed graphs.
|AnswerD=Mean > Mode > Median
|AnswerD=Mean > Mode > Median
|AnswerDExp=This is not the relationship in negatively skewed graphs.
|AnswerDExp=This is not the relationship in positively skewed graphs.
|AnswerE=Mode > Mean > Median
|AnswerE=Mode > Mean > Median
|AnswerEExp=This is not the relationship in negatively skewed graphs.
|AnswerEExp=This is not the relationship in positively skewed graphs.
|RightAnswer=B
|RightAnswer=C
|WBRKeyword=median, mode, mean, negatively, positively, skew, skewed, graph, negative, positive, normal, distribution, greater, smaller, larger, less, Gaussian, omeprazole, reflux, gastroesophageal, disease, GERD, dose, experiment
|WBRKeyword=median, mode, mean, negatively, positively, skew, skewed, graph, negative, positive, normal, distribution, greater, smaller, larger, less, Gaussian, omeprazole, reflux, gastroesophageal, disease, GERD, dose, experiment
|Approved=No
|Approved=No
}}
}}

Revision as of 06:18, 24 October 2013
Author [[PageAuthor::Rim Halaby, M.D. [1]]]
Exam Type ExamType::USMLE Step 1
Main Category MainCategory::Biostatistics/ Epidemiology
Sub Category SubCategory::Gastrointestinal
Prompt [[Prompt::A researcher is studying the optimal dose of omeprazole required for relief of gastroesophageal reflux disease symptoms (GERD). For his experiment, he enrolled 240 patients known to have GERD who complain of similar symptoms. The patients first receive a dose of 10 mg of omeprazole by mouth, and incremental increase by 5 mg is added for patients who do not report symptomatic relief. The optimal dose of omepraozale is documented as the minimum dose at which the subjects report relief. Following data collection, the researcher demonstrates his findings on the graph shown below. Based on his findings, which of the following statements regarding the mean, median, and mode is correct?

400px]]

Answer A [[AnswerA::Median > Mode > Mean]]
Answer A Explanation AnswerAExp::This is not the relationship in positively skewed graphs.
Answer B [[AnswerB::Mode > Median > Mean]]
Answer B Explanation AnswerBExp::This would be a correct answer in negatively skewed graphs.
Answer C [[AnswerC::Mean > Median > Mode]]
Answer C Explanation AnswerCExp::This is the correct relationship between mean, median, and mode in positively skewed graphs.
Answer D [[AnswerD::Mean > Mode > Median]]
Answer D Explanation AnswerDExp::This is not the relationship in positively skewed graphs.
Answer E [[AnswerE::Mode > Mean > Median]]
Answer E Explanation AnswerEExp::This is not the relationship in positively skewed graphs.
Right Answer RightAnswer::C
Explanation [[Explanation::Based on the graph above, the distribution of the researcher's findings show a positively skewed graph because the tail of the graph is towards the positive side. In such graphs, the relationship of the mean, median, and mode are always as follows: mean > median > mode.

In contrast, a negatively skewed graph, where the tail is towards the more negative values, the relationship is always as follows: mode > median > mean. Notably, in both positively and negatively skewed graphs, the median is always in the middle.

Graphs with normal distribution typically have mean = median = mode.

Educational Objective: Positively skewed graphs, with the tail towards the more positive side, always have mean > median > mode.
Educational Objective:
References: ]]

Approved Approved::No
Keyword WBRKeyword::median, WBRKeyword::mode, WBRKeyword::mean, WBRKeyword::negatively, WBRKeyword::positively, WBRKeyword::skew, WBRKeyword::skewed, WBRKeyword::graph, WBRKeyword::negative, WBRKeyword::positive, WBRKeyword::normal, WBRKeyword::distribution, WBRKeyword::greater, WBRKeyword::smaller, WBRKeyword::larger, WBRKeyword::less, WBRKeyword::Gaussian, WBRKeyword::omeprazole, WBRKeyword::reflux, WBRKeyword::gastroesophageal, WBRKeyword::disease, WBRKeyword::GERD, WBRKeyword::dose, WBRKeyword::experiment
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