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Measures of Central Tendency

A research team at a large university hospital has just completed a pilot study of an innovative new treatment that is intended to be used to treat patients in the later stages of prostate cancer. They had 12 patients, males, ranging in age from 47 to 73. All had been diagnosed as in stage 4 of the disease within 4 weeks of agreeing to participate in the study. Here from lowest to highest, are the number of weeks that the patients lived after treatment began:

3, 5, 6, 6, 8, 8, 9, 9, 9, 10, 11, 45

The mean number of weeks that a prostate cancer patient lives after receiving a confirmed diagnosis of being in stage 4 is 9.6 (with a standard deviation of 3.2)

The researchers were overjoyed that the mean number of weeks that the patients in this study survived was 10.75 with a standard deviation of 11.02. They are presenting this result to the committee in charge of distributing grant money to researchers in the hospital.

Pretend you are on the committee and write a statement expressing your views on the level of promise that this study shows. Comment on measures of central tendency and under what conditions the different types should be used, the meaning of the standard deviation, and any other relevant comments you would have if you were a member of the committee evaluating this study to determine if more money should be granted to these researchers.

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RESPONSE:

A research team at a large university hospital has just completed a pilot study of an innovative new treatment that is intended to be used to treat patients in the later stages of prostate cancer. They had 12 patients, males, ranging in age from 47 to 73. All had been diagnosed as in stage 4 of the disease within 4 weeks of agreeing to participate in the study. Here from lowest to highest, are the number of weeks that the patients lived after treatment began:

3, 5, 6, 6, 8, 8, 9, 9, 9, 10, 11, 45

1. The mean number of weeks that a prostate cancer patient lives after receiving a confirmed diagnosis of being in stage 4 is 9.6 (with a standard deviation of 3.2)

In other words, the range of weeks was 9.6 plus or minus 3.2 or (6.4 t0 12.8).

2. The researchers were overjoyed that the mean number of weeks that the patients in this study survived was 10.75 with a standard deviation of 11.02. They are presenting this result to the committee in charge of distributing grant money to researchers in the hospital.

These researchers found a high degree of variance considering the large standard deviation (11.02). In other words, the range of weeks was (-0.27 to 22.77). The mean (10.75) would not be ...

Solution Summary

This solution examines measures of central tendency within a study and expresses the level of promise that this study shows. It also comment on measures of central tendency and under what conditions the different types should be used, the meaning of the standard deviation, and any other relevant comments.

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