2.1-2.3

Question 1

Define class

Answer 1

A class is one of the categories into which qualitative data can be classified.

Question 2

Define class frequency

Answer 2

The class frequency is the number of observations in the data set that fall into a particular class.

Question 3

Define class relative frequency and give the formula.

Answer 3

The class relative frequency is the class frequency divided by the total number of observations in the data set; that is,
class relative frequency = class frequency/n

Question 4

Define class percentage and give the formula.

Answer 4

The class percentage is the class relative frequency multiplied by 100; that is,
Class percentage = (class relative frequency)*100

Question 5

Describe a bar graph.

Answer 5

The categories (classes) of the qualitative variable are represented by bars, where the height of each bar is either the class frequency, class relative frequency, or class percentage.

Question 6

Describe a pie chart.

Answer 6

The categories (classes) of the qualitative variable are represented by slices of a pie (circle). The size of each slice is proportional to the class relative frequency.

Question 7

Describe a Pareto diagram.

Answer 7

A bar graph with the categories (classes) of the qualitative variable (i.e., the bars) arranged by height in descending order from left to right.

Question 8

What are three graphical methods for describing quantitative data?

Answer 8

dot plots, stem-and-leaf displays, and histograms

Question 9

What is a benefit of a stem and leaf and a dot plot display as compared to a histogram?

Answer 9

Histograms do not let us identify individual measurement. While they are visible to some extent in a dot plot and clearly visible in a stem and leaf display. Since STALDs arranges the data in ascending order, it is easy to locate individual measurements.

Question 10

Describe a dot plot.

Answer 10

The numerical value of each quantitative measurement in the data set is represented by a dot on a horizontal scale. When data values repeat, the dots are placed above one another vertically.

Question 11

Describe a stem and leaf display.

Answer 11

The numerical value of the quantitative variable is partitioned into a “stem” and a “leaf.” The possible stems are listed in order in a column. The leaf for each quantitative measurement in the data set is placed in the corresponding stem row. Leaves for observations with the same stem value are listed in increasing order horizontally.

Question 12

Describe a histogram.

Answer 12

The possible numerical values of the quantitative variable are partitioned into class intervals, each of which has the same width. These intervals form the scale of the horizontal axis. The frequency or relative frequency of observations in each class interval is determined. A vertical bar is placed over each class interval, with the height of the bar equal to either the class frequency or class relative frequency.

Question 13

What is the central tendency of a set of measurements?

Answer 13

the tendency of the data to cluster, or center, about certain numerical values.

Question 14

What is the variability of a set of measurements?

Answer 14

, the spread of the data

Question 15

What is the most popular and best understood measure of central tendency for quantitative data sets?

Answer 15

The most popular and best understood measure of central tendency for a quantitative data set is the arithmetic mean.

Question 16

Define the mean.

Answer 16

The mean of a set of quantitative data is the sum of the measurements, divided by the number of measurements contained in the data set.

Question 17

What are the symbols for sample mean and population mean>

Answer 17

x = sample mean
mu = population mean

Question 18

What factors influences how accurately x estimates mu?

Answer 18

1. Size of the sample (larger samples = more accurate)
2. Variability/spread of data (more variable = less accurate)

Question 19

What is the median?

Answer 19

The median of a quantitative data set is the middle number when the measurements are arranged in ascending (or descending) order.

Question 20

How do you calculate the median of a sample?

Answer 20

Arrange the n measurements from the smallest to the largest.

If n is odd, M is the middle number.

If n is even, M is the mean of the middle two numbers.

Question 21

What are the symbols for sample and population mean?

Answer 21

M = sample n = population

Question 22

Between median and mean, which is more sensitive to extremely large or small measurements?

Answer 22

Mean.

Question 23

What does it mean if a data set is skewed?

Answer 23

A data set is said to be skewed if one tail of the distribution has more extreme observations than the other tail.

Question 24

What is the mode?

Answer 24

The mode is the measurement that occurs most frequently in the data set.

Question 25

What type of data is the mode particularly useful for?

Answer 25

Qualitative

Question 26

What is the modal class?

Answer 26

The measurement class containing the largest relative frequency is called the modal class.

Question 27

What does the choice of measurement of central tendency depend on?

Answer 27

The choice of which measure of central tendency to use will depend on the properties of the data set analyzed and the application of interest. Consequently, it is vital that you understand how the mean, median, and mode are computed.