Need help with a Statistics question?

Question

I'm not exactly sure how to do this particular problem I don't know why kind of graph I'm supposed to use. Thanks for any help!

Question:
Listed below are the survival times in days of 72 guinea pigs after they were injected with infectious bacteria in a medical experiment. Survival times, whether of machines under stress or cancer patients after treatment, usually have distributions that are skewed to the right.

Data:
43, 45, 53, 56, 56, 57, 58, 66, 67, 73, 74, 79, 80, 80, 81, 81, 81, 82, 83, 84, 88, 89, 91, 91, 92, 92, 97, 99, 99, 100, 100, 101, 102, 102, 102, 103, 104, 107, 108, 109, 113, 114, 118, 121, 123, 126, 128, 137, 138, 139, 144, 145, 147, 156, 162, 174 178, 179, 184, 191, 198, 211, 214, 243, 249, 329, 380, 403, 511, 522, 598

(a) Graph the distribution and describe its main features. Does it show the expected right shew?
(b) Which numerical summary would you choose for these data? Calculate your chosen summary. How does it reflect the skewness of the distribution

Answer 1

Since there is only one type of data (survival time), the data can only be graphed as a bar graph showing the frequency of the different survival times. To do this, you need to divide the data into maybe 5- 7 categories, and count the number of animals in each category. The X-axis lists the categories (maybe something like intervals of 50: 0-50; 51-100; 101-150, etc). The Y-axis is the number of animals that are observed in each of the categories.

Answer 2

You need a histogram. Categorize the data into segments: 0-50, 51-100, etc. Plot the frequency in each. You will see a right skew.

I'm not sure what (b) is referring to. It seems like a list to choose from. To numerically describe the data, you need the mean, the standard deviation and a measure of skew.

Answer 3

the data is skewed to the right, a lot. so i would use the median and non-parametric estimators to give a more useful data analysis.

mean = 142.7
median = 103