Question

thirty-nine women with a diagnosis of inoperable or metastatic breast cancer have been followed-up for a number of years, while under continuous treatment with a medication called trastuzumab. the time (in months) each patient remained in remission was recorded. Remission is a decrease or disappearance of signs and symptoms of cancer. Below is the data.

50 74 35 39 21 37 27 35 30 35 26 38 34 34 26 41 61 33 33 26 25 41 35 34 44 33 60 61 42 30 80 31 24 49 26 31 28 41 37

Are there any outliers in the sample?

Compute the 45th percentile of the remission time.

Find a 97% confidence interval of the average remission time

Answer 1

#outlines

Minimum: 21

Maximum: 80

Median: 35

Quartile Q1: 30

Quartile Q3: 41

Lower fence: 13.5

Upper fence: 57.5

Set of outliers: {60, 61, 61, 74, 80}

#

45^th percentile = 34

Solution:

Step 1. Arrange the data in ascending order: 21, 24, 25, 26, 26, 26, 26, 27, 28, 30, 30, 31, 31, 33, 33, 33, 34, 34, 34, 35, 35, 35, 35, 37, 37, 38, 39, 41, 41, 41, 42, 44, 49, 50, 60, 61, 61, 74, 80

Step 2. Compute the position of the p^th percentile (index i):

i = (p / 100) * n), where p = 45 and n = 39

i = (45 / 100) * 39 = 17.55

Step 3. The index i is not an integer, round up. (i = 18) ⇒ the 45^th percentile is the value in 18^th position, or 34

Answer: the 45^th percentile is 34

#

please like ??