A particular brand of batteries has a mean lifetime of 58.4 months, with a standard deviation of 5.2 months. A sample of 12 batteries was taken and their lifetimes, in months, are recorded.

56.3 59.2 61.8 43.1 68.8 51.2

58.5 56.4 64.2 66.9 49.0 60.1

a) Calculate the median, first quartile, and third quartile for these data. Determine the range and interquartile range.

b) Calculate the mean, variance, and standard deviation ( use the population formula).

c) Compare the average lifetime and spread of the sample to those of the population given in the question.