Question

In: Statistics and Probability

The table below shows the means and standard deviations of the survival times (in days) of...

The table below shows the means and standard deviations of the survival times (in days) of some cancer patients who were treated with the same medication. Use these statistics to answer the question below.

Type of Cancer Patient

Mean

Standard Deviation

Breast

1395.9

1239.0

Bronchial

211.6

209.9

Colon

457.4

427.2

Ovarian

884.3

1098.6

Stomach

286.0

346.3

Which type of cancer patients

     (a) had the highest average survival time?  

     (b) had the lowest average survival time?  

     (c) had the most consistent survival times (least variation)?  

     (d) had the least consistent survival times (most variation)?  

     (e) had a standard deviation that was almost equal to the mean?

     (f) Colon cancer patients’ survival times were less / more consistent than stomach cancer patients’ survival times.  

     (g) On average, ovarian cancer patients’ survival times differed from 884.3 days by about  .

     (h) A breast cancer patient had a survival time of 1000 days. Was this within one standard deviation of the mean or was it further out? Enter "within" or "further out".  

Solutions

Expert Solution

Answer a) Breast cancer patients

Based on table, it can be said that Breast cancer patients had the highest average survival time (1395.9 days)

Answer b) Bronchial cancer patients

Based on table, it can be said that Bronchial cancer patients had the lowest average survival time (211.6 days)

Answer c) Breast cancer patients

We have compared coefficient of variation to compare variation relative to mean. Following is the table showing coefficient of variation for each cancer type. The CV have been calculated using following formula:

CV = (SD/Mean)*100

Based on CV table, it can be said that Breast cancer patients had the most consistent survival times (88.8%)

Answer d) Ovarian cancer patients

Based on CV table, it can be said that Ovarian cancer patients had the least consistent survival times (124.2%)

Answer e) Bronchial cancer patients​​​​​​​

Based on CV table, it can be said that Bronchial cancer patients had a standard deviation that was almost equal to the mean (99.2%)

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orchestra answered 2 years ago
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