7.1: Describing Data Sets

Question 1

Describe the term “statistics”.

Answer 1

Statistics is used to refer to data and the methods used to analyze data.

Question 2

The two categories of statistical methods? Describe.

Answer 2

1. Descriptive statistics summarize the important characteristics of large data sets.
2. Inferential statistics pertain to procedures used to make forecasts, estimates or judgments about a large set of data on the basis of a sample.

Question 3

What is a population?

Answer 3

A population is the set of all possible members of a stated group.

Question 4

What is a sample?

Answer 4

A sample is defined as a subset of the population of interest. Sample is drawn from the population, and the sample’s characteristics can be used to describe the population as a whole.

Question 5

What are the four types of measurement scales? NOIR

Answer 5

1. Nominal scales (least information, no particular order)
2. Ordinal scales (relative ranking ie. #1 as best #10 as worst)
3. Interval scales (relative ranking + assurance that differences between scale values are equal ie. temperature)
4. Ratio scales (relative ranking + equal differences between scale values + true zero point as the origin ie. money)

Question 6

What is a parameter?

Answer 6

A parameter is a measure used to describe a characteristic of a population (like mean return/standard deviation).

Question 7

What is a sample statistic?

Answer 7

A sample statistic is a measure used to describe a characteristic of a sample.

Question 8

What is a frequency distribution?

Answer 8

A frequency distribution is a tabular presentation of statistical data that aids the analysis of large data sets, which summarizes statistical data by assigning it to specific groups/intervals/classes. Data employed with a frequency distribution may be measured using any type of measurement scale.

Question 9

What are the 3 steps (DTC) used to construct a frequency distribution? What are the 5 conditions of the first step?

Answer 9

Step 1: Define the intervals. Conditions for the range values for each interval:

• Lower and upper limit
• All inclusive
• Nonoverlapping
• Mutually exclusive
• The total set of intervals should cover the total range of values for the entire population

Step 2: Tally the observations (assign to appropriate interval).

Step 2: Count the observations (the number of observations that are assigned to each interval).

Question 10

What is absolute frequency?

Answer 10

Absolute frequency is the actual number of observations that fall within a given interval.

Question 11

What is modal interval?

Answer 11

Modal frequency is the interval with the greatest frequency in a frequency distribution.

Question 12

What is relative frequency?

Answer 12

Relative frequency is the percentage of total observations falling within each interval, calculated by the absolute frequency in an interval/total number of observations.

Question 13

What is cumulative absolute frequency?

Answer 13

For any given interval, cumulative absolute frequency is the sum of the absolute or relative frequencies up to and including the given interval.

Question 14

What is cumulative relative frequency?

Answer 14

Cumulative relative frequency the sum of relative frequencies starting at the lowest interval to the highest (up to and including the given interval).

Question 15

What is a histogram? What is its attractive feature? What is on the x-axis? Y-axis?

Answer 15

Histogram is a graphical presentation of absolute frequency distribution presented as a bar chart of continuous data that has been classified into a frequency distribution.

Attractive feature is that it allows us to see where most of the observations are concentrated.

X-axis is interval. Y-axis is frequency.

Question 16

What is a frequency polygon? What’s on the x-axis and y-axis?

Answer 16

Frequency polygon is a graphical presentation that plots the midpoint of each interval on the horizontal axis, while the absolute frequency for that interval is plotted on the vertical axis. Each point is then connected with a straight line.

Question 17

Define parameter.

Answer 17

Parameter is a measure used to describe a characteristic of a population (such as mean return and the standard deviation of returns).

Question 18

Define sample statistic.

Answer 18

Similar to a parameter. Used to measure the characteristic of a sample.

Question 19

What is a frequency distribution?

Answer 19

Frequency distribution is a tabular presentation of statistical data that aids that analysis of large data sets, which summarize statistical data by assigning it to specified groups (intervals).