Question

2. Six Flags Magic Mountain is studying the demographics of its visitors. A sample of visitors is selected and their ages recorded:

   30, 14, 26, 21, 38, 9, 17, 29

   1. a) Calculate the sample mean.

   2. b) Calculate the sample standard deviation.

   3. c) Find the mode(s).

   4. d) Find the 5 number summary.

   5. e) Calculate the IQR.

Answer 1

Following table shows the calculations:

	X	(X-mean)^2
	9	196
	14	81
	17	36
	21	4
	26	9
	29	36
	30	49
	38	225
Total	184	636

Sample size: n=8

a)

The sample mean is

b)

The sample standard deviation is

c)

Since all values are unique so there is no mode of the data.

d)

Minimum : 9

First quartile: Since first half of data set has 4 data values so it is average of 2nd and 3rd data values. So

Median: It is average of 4th and 5th data values. So

Third quartile: Since second half of data set has 4 data values so it is average of 6th and 7th data values. So

Maximum: 38

e)

The inter quartile range is