CK-12 Probability and Statistics - Advanced

1.4. Measures of Spread http://www.ck12.org

Standard Deviation

A measure of the “typical” distance of all the data points in a set from the mean.

Population Standard Deviation

The square root of the result of dividing the sum of the squared deviations by the population size.

Sample Standard Deviation

The square root of the result of dividing the sum of the squared deviations by one less than the sample size.

Variance

The square of the standard deviation.

Part One: Multiple Choice

1. Which of the following is true for any set of data?
   a. The range is a resistant measure of spread.
   b. The standard deviation is not resistant.
   c. The range can be greater than the standard deviation.
   d. The IQR is always greater than the range.
   e. The range can be negative.


2. The following shows the mean number of days of precipitation by month in Juneau Alaska:

TABLE1.13: Mean Number of Days With Precipitation >0.1 inches

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

18 17 18 17 17 15 17 18 20 24 20 21

Source:http://www.met.utah.edu/jhorel/html/wx/climate/daysrain.html (2/06/08)

Which month contains the median number of days of rain?

(a) January

(b) February

(c) June

(d) July

(e) September

3. Given this set of data: 2, 10 , 14 ,6; Which of the following is equivalent to ̄x?
   a. mode
   b. median
   c. midrange
   d. range
   e. None of these


4. Place the following in order from smallest to largest. I. Range II. Standard Deviation III. Variance
   a. I, II, III
   b. I, III, II