UL MBA Stats - Chapter 2

regarding freq tables and freq distribution, which of the following is true?

both show the number of observations in each class

mutually exclusive classes

the classes don't overlap

frequency table

frequency tables only list QUALITATIVE data

which of the following is a feature of a relative frequency distribution

the sum of relative frequencies must be one (assuming no rounding errors)

collective exhaustive classes

there is a class for each observation

bar chart

A graph that shows qualitative classes on the horizontal axis and the frequencies on the vertical axis. The class frequencies are proportional to the heights of the bars.

frequency distribution

A grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class

Which of the following is an advantage of a cumulative frequency polygon over a histogram or frequency polygon? -it can show the number of observations in a given class -it can show the total number of observations less than a particular class' upper limit -it shows class midpoints as points on the polygon

-it can show the total number of observations less than a particular class' upper limit

Match the term with the definition -mutually exclusive classes -collective exhaustive classes -the classes don't overlap -there is a class for each observation

mutually exclusive classes- the classes don't overlap collective exhaustive classes- there is a class for each observation

Which of the following can be observed from a histogram? Check all that apply. -the spread of the data -the relationship between two variables -the shape of the distribution -the approximate number of observations -the concentration of the data

-the spread of the data -the shape of the distribution -the approximate number of observations -the concentration of the data

Step 1 to create a frequency distribution

Decide the total number of classes. A useful recipe to determine the number of classes (k) is the "2 to the k rule." This guide suggests you select the smallest number (k) for the number of classes such that 2^k (in words, 2 raised to the power of k) is greater than the number of observations (n).

cumulative relative frequency distribution

Shows the percent of observations less than a given value.

Suppose that the miles per gallon for 80 cars is summarized in a frequency distribution. Below is a part of the distribution. What would the relative frequency be for the class "20 up to 24"? MPG Frequency 16 up to 20 10 20 up to 24 16 -80 -0.125 -10 -0.20 -16 -1.00

-0.20

pie chart

A chart that shows the proportion or percentage that each class represents of the total number of frequencies.

histogram

A graph in which the classes are marked on the horizontal axis and the classes are marked on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars, and the bars are drawn adjacent to each other

Step 2 to create a frequency distribution

Determine the class interval. Generally, the class interval is the same for all classes. The classes all taken together must cover at least the distance from the minimum value in the data up to the maximum value. Expressing these words in a formula: i>= (Maximum Value - Minimum Value)/ k where i is the class interval, and k is the number of classes

frequency distribution

Does NOT summarize qualitative data, only Quantitative

cumulative frequency distribution

Scale the upper limit of each class along the X-axis and the corresponding cumulative frequencies along the y-axis. To provide additional information, you can label the vertical axis on the right in terms of cumulative relative frequencies.

frequency polygon

Shows the shape of the distribution and is similar to a histogram. It consists of line segments connecting the points formed by the intersections of the class midpoints and the class frequencies. The midpoint of each class is scaled on the X-axis and the class frequencies on the Y-axis.

class frequency

the number of observations in each class

Suppose you are trying to summarize the data set with a maximum value of 70 and a minimum value of 1. If you decide to use seven classes, which one of the following would be a reasonable class interval? -10 -1 -7 -70

10

Suppose a frequency distribution has the following consecutive classes: $20 up to $30 $30 up to $ 40 $40 up to $50 What is the midpoint for the first class? -$25 -$10 -$20 -$30

$25

What is the final step is creating a frequency distribution? -decide the number of classes -set the individual class limits -count the number of observations in each class -determine class width

-count the number of observations in each class

Which of the following practices is commonly used in setting class limits for a frequency distribution? -overlapping the upper limit with the lower limit of the next higher class -rounding the class size up -deleting data which is too low or too high to fit convenient intervals -placing "excess" interval width equally in the two tails of the distribution

- rounding the class size up -placing "excess" interval width equally in the two tails of the distribution

frequency table

a grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class

which of the following is true about pie charts?

the size of a slice should represent a classes relative frequency

Which of the following is not part of a histogram? -quantitative data divided into classes -adjacent bars whose height represents the number of frequencies -the frequency of occurence of data within a class -the frequency of occurence of a nominal variable

-the frequency of occurence of a nominal variable

Which of the following is the best definition of "class midpoint"? -halfway between the lower or upper limits of two consecutive classes -the average value of the observations in the class interval -halfway between the highest and lowest classes

-halfway between the lower or upper limits of two consecutive classes

Which of the following features is an advantage that the frequency polygon has over the histogram? -it can directly compare two or more frequency distributions -it depicts each class as a rectangle, with the height representing the number of observations -the frequency polygon show relative frequencies with respect to a circle, not bars

-it can directly compare two or more frequency distributions

Step 3 to create a frequency distribution

Set the individual class limits. State clear class limits so you can put each observation into only one category. This means you must avoid overlapping to unclear class limits

In using the "2 to the k rule" to determine the number of classes for a frequency distribution, what is the meaning of the value k? -k is the greatest number of classes such that 2^k < n where n is the number of observations -k is the smallest number of classes such that 2^k is greater than the number of observations -k is the number of observations which is to be summarized

-k is the smallest number of classes such that 2^k is greater than the number of observations

Which two of the following practices is commonly used in setting class limits for a frequency distribution? -deleting data which is too low or too high to fit convenient intervals -overlapping the upper limit with the lower limit of the next higher class -placing "excess" interval with equally in the two tails of the distribution -rounding the class size up

-placing "excess" interval with equally in the two tails of the distribution -rounding the class size up

A relative frequency distribution shows: -the fraction or percentage of observations in each class interval -the number of observations in each class interval -the number of observations of a particular value in a set of data

-the fraction or percentage of observations in each class interval

the value shown on the vertical axis of a cumulative frequency polygon for a particular class is found by

counting the numbers of observations less than the upper limit of the class

The number of observations in each class is called the class ____________. -limit -interval -midpoint -frequency

frequency

to divide data with a high value of H and a low value of L into K classes, the class interval must be

at least (H/L)/k

Regarding frequency tables and frequency distributions, which one of the following is true? -only frequency distributions use mutually exclusive classes -both show the number of observations in each class -only frequency tables use collectively exhaustive classes

-both show the number of observations in each class

The value shown on the vertical axis of a cumulative frequency polygon for a particular class is found by: -counting the number of observations less than the upper limit of the class -counting the number of observations less than the upper limit of the class -dividing the class frequency by the total number of observations

-counting the number of observations less than the upper limit of the class

class midpoint

Halfway between the lower or upper of two consecutive classes. It is computed by adding the lower or upper limits of consecutive classes and dividing by 2.

Advantage of the frequency polygon over the histogram

It allows us to compare directly two or more frequency distributions.

Which of the following are characteristics of bar charts? -bar charts are used for qualitative data -plotted rectangles should be the same width -plotted rectangles should be the same height -there should be gaps between the bars

-bar charts are used for qualitative data -plotted rectangles should be the same width -there should be gaps between the bars

A business statistics course has 2 accounting majors, 4 finance majors, 6 marketing majors, and 8 insurance majors. Which one of the following is true if a pie chart was constructed to depict majors of students? -the slice for marketing majors would be two times as big as the finance slice -the slice for accounting would represent 20% of the pie char -the slice for insurance would make up more than half of the pie chart - the marketing slice would be three times as big as the accounting slice

- the marketing slice would be three times as big as the accounting slice

Place the following steps used in constructing a frequency distribution into correct order. -tally the number of observations in each class -decide on the number of classes -determine class width -set individual class limits

-determine the number of classes -determine the class width -set individual class limits -tally the number of observations in each class

A frequency distribution table shows the number of observations for each class interval of data. How is this data plotted as a frequency polygon? -frequency is plotted on the horizontal axis and the class interval is plotted on the vertical axis -frequency is plotted on the vertical axis and the class midpoint is plotted on the horizontal axis -frequency is plotted on the vertical axis and the class interval is plotted on the horizontal axis -the cumulative proportion of observations for each class is plotted on the vertical axis and the class upper limit is plotted on the horizontal axis

-frequency is plotted on the vertical axis and the class midpoint is plotted on the horizontal axis

Which of the following is not a characteristic of a frequency distribution? -It displays the number of observations in each class -it summarizes qualitative data -it uses mutually exclusive classes -it uses collectively exclusive classes

-it summarizes qualitative data

Which one of the following is regarding raw data? -raw data are the tally of data in each class -raw data refers to the form of the data after grouping has taken place -raw data are the result of dividing frequencies by the total number of observations -raw data are simply a listing of data before summarizing it

-raw data are simply a listing of data before summarizing it

Which of the following can be observed from a histogram? Check all that apply. -the approximate number of observations -the spread of the data -the relationship between two variables -the concentration of the data -the shape of the distribution

-the approximate number of observations -the spread of the data -the concentration of the data -the shape of the distribution

convert a frequency distribution to a relative frequency distribution

each class frequencies is divided by the total number of observations