Question

Problem 3. (15 points) Given the following data: 3, 2, 3, 4, 5, 3, 4, 6, 4, 10, 7, 11 () (2 points) Calculate the sample mean by hand using its definition. Round your in results to two decimal places and your final answer to one decimal place. Same for the remai questions. (2) (2 points) Calculate the median of the data. (3) (3 points) Calculate the sample variance by hand using its definition. 4) (3 poi ning ints) Calculate the sample variance by skipping the sample mean and using the Sx formula that we covered in Lecture 2 (Slide 41). (5) (2 points) Calculate the sample standard deviation. (6) (3 points) the Calculate the interquartile mean (i.e., trimmed mean with 96-25%).

Answer 1

Following table shows the ordered data set, sum of data values and calculations for standard deviation:

So we have

1:

The sample mean is:

2:

There are 12 data values so median will be average of 6th and 7th data value. That is median will be

3:

4:

5:

6:

Since 12 * 0.25 = 3 so we need to trim 3 data from both sides of ordered data set. The new data set and sum of remaining data values is as follows:

So,