Chapter 3 Describing Data Using Numerical Measures

Question 1

Parameter

Answer 1

A measure computed from the entire population. As long as the population does not change, the value of the parameter will not change.

Question 2

Statistic

Answer 2

A measure computed from a sample that has been selected from a population. The value of the statistic will depend on which sample is selected.

Question 3

Mean

Answer 3

A numerical measure of the center of a set of quantitative measures computed by dividing the sum of the values by the number of values in the data.

Question 4

Population Mean

Answer 4

The average for all values in the population computed by the dividing the sum of all values by the population size.

Question 5

Sample Mean

Answer 5

The average for all values in the sample computed by dividing the sum of all sample values by the sample size.

Question 6

Median

Answer 6

The median is a center value that divides a data array into two halves. We use “U” to denote the population median and “M” to denote the sample median.

Question 7

Data Array

Answer 7

Data that have been arranged in numerical order.

Question 8

Symmetric Data

Answer 8

Data sets whose values are evenly spread around the center. For symmetric data, the mean and median are equal.

Question 9

Skewed Data

Answer 9

Data sets that are not symmetric. For skewed data, the mean will be larger or smaller than the median.

Question 10

Right-Skewed Data

Answer 10

A data distribution is right skewed if the mean for the data is larger than the median.

Question 11

Left-Skewed Data

Answer 11

A data distribution is left skewed if the mean for the data is smaller than the median.

Question 12

Mode

Answer 12

The mode is the value in a data set that occurs most frequently

Question 13

Weighted Mean

Answer 13

The mean value of data values that have been weighted according to their relative importance.

Question 14

Percentiles

Answer 14

The Pth percentile in a data array is a value that divides the data set into two parts. The lower segment contains at least P% and the upper segment contains at least (100-P)% of the data. The 50th percentile is the median.

Question 15

Quartiles

Answer 15

Quartiles in a data array are those values that divide the data set into four equal-sized groups. The median corresponds to the second quartile.

Question 16

Box and Whisker Plot

Answer 16

A graph that is composed of two parts: a box and the whiskers. The box has a width that ranges from the first quartile (Q1) to the third quartile (Q3). A vertical line through the box is placed at the median. Limits are located at a value that is 1.5 times the difference between Q1 and Q3 below Q1 and above Q3. The whiskers extend to the left to the lowest value within the limits and to the right to the highest value within the limits.

Question 17

Variation

Answer 17

A set of data exhibits variation if all the data are not the same value.

Question 18

Range

Answer 18

The range is a measure of variation that is computed by finding the difference between the maximum and minimum values in a data set.

Question 19

Interquartile Range

Answer 19

The interquartile range is a measure of variation that is determined by computing the difference between the third and first quartiles.

Question 20

Variance

Answer 20

The population variance is the average of the squared distances of the data values from the mean.

Question 21

Standard Deviation

Answer 21

The standard deviation is the positive square root of the variance.

Question 22

Coefficient of Variation

Answer 22

The ratio of the standard deviation to the mean expressed as a percentage. The coefficient of variation is used to measure variation relative to the mean.