Question

1) Why would one use the median instead of the mean?

2) An experiment involves rolling a six-sided die 480 times and recording the number of 3s. What is the mean and standard deviation?

3) In a normal distribution, what is the percentage of data having a z score less than -1?

4) We roll 5 six-sided die. What is the probability of obtaining exactly two 1s?

5) What is sampling error, and how would you distinguish it from nonsampling error?

6) What types of inferences can we make?

Answer 1

We would be looking at the first 4 questions here as:

Q1) Median gives the middle value of a set of data given the data is arranged in ascending order. Therefore whenever there are extreme values on either side ( lower or higher side), median wont be affected by it while mean takes into consideration all the values and so with outliers, mean would not given a good indication of central tendency here. Therefore in presence of data outliers, median is a good measure.

Q2) The number of 3s in 480 trials could be modelled here as:

The mean and standard deviation thus are computed here as:

Q3) The percentage of data below a z score of -1 is obtained from the standard normal tables as:
= P(Z < -1)

= 0.1587

Therefore 0.1587 is the required percentage here.

Q4) The probability that exactly two 1as happen in 5 rolls is computed using the binomial probability function as:

Therefore 0.1608 is the required probability here.