Chapter 2: Organizing and Summarizing Data

Question 1

What is frequency distribution?

Answer 1

Frequency Distribution lists each category of data and the number of occurrences for each category of data.

Question 2

What does a frequency distribution table look like?

Answer 2

Question 3

What is relative frequency?

Answer 3

Relative Frequency is the proportion (or percent) of observations within a category and is found using the formula:

frequency/sum of all frequencies = relative frequency

Question 4

How is a relative frequency table organized?

Answer 4

A relative frequency distribution table lists each category of data with the relative frequency.

Question 5

What is a bar graph?

Answer 5

A bar graph is constructed by labeling each category of data on either the horizontal or vertical axis and the frequency or relative frequency of the category on the other axis.

Rectangles of equal width are drawn for each category. The height of each rectangle represents the category’s frequency or relative frequency.

Question 6

What is a Pareto Chart?

Answer 6

A Pareto chart is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency

Question 7

What graph should you use to compare data?

Answer 7

A side by side bar graph

Data sets should be compared using relative frequencies, because different sample or population sizes make comparisons using frequencies difficult or misleading.

Question 8

Can Bar Graphs be drawn horizontally?

Answer 8

Yes, horizontal bars are preferred when category names are lengthy.

Question 9

What is a Pie Chart?

Answer 9

A pie chart is a circle divided into sectors. Each sector represents a category of data. The area of each sector is proportional to the frequency of the category.

Question 10

What is the first step to summarizing quantitative data on a display?

Answer 10

The first step in summarizing quantitative data is to determine whether the data are discrete or continuous.

*Discrete: can be counted *Continuous: is measured.

Discrete and few different values of the variable - the categories of the data (classes) will be the observations (as in qualitative data)

Continous Data - the categories of data (classes) must be created using intervals of numbers. Also applies if there are too many variables in discrete data.

Question 11

What is a histogram?

Answer 11

A histogram is constructed by drawing rectangles for each class of data.

The height of each rectangle is the frequency or relative frequency of the class.

The width of each rectangle is the same and the rectangles touch each other.

Question 12

What does constructing Frequency and Relative Frequency Distribution from Discrete Data look like?

Answer 12

EXAMPLE: The following data represent the number of available cars in a household based on a random sample of 50 households. Construct a frequency and relative frequency distribution.

3 0 1 2 1 1 1 2 0 2

4 2 2 2 1 2 2 0 2 4

1 1 3 2 4 1 2 1 2 2

3 3 2 1 2 2 0 3 2 2

2 3 2 1 2 2 1 1 3 5

Question 13

What are classes?

Answer 13

Classes are categories into which data are grouped.

*When a data set consists of a large number of different discrete data values or when a data set consists of continuous data, we must create classes by using intervals of numbers.

Question 14

When reading a Data Table -

What is a Lower Class Limit?

What is a Upper Class Limit?

What is the Class Width?

Answer 14

lower class limit of a class is the smallest value within the class

upper class limit of a class is the largest value within the class

class width is the difference between consecutive lower class limits

Example from chart:

Lower class limit of 1st class = 25

Upper class limit of 1st class = 34

Class width between categories 35-25=10

Question 15

Example of organized continuous data on table?

Answer 15

Example of continuous data on table:

The following data represent the time between eruptions (in seconds) for a random sample of 45 eruptions.

The smallest data value is 672 and the largest data value is 738. We will create the classes so that the lower class limit of the first class is 670 and the class width is 10 and obtain the following classes:’

670 − 679

680 − 689 etc.

Question 16

What are the guidelines for determining the Lower Class Limit of the First Class and Class Width?

Answer 16

Choosing the Lower Class Limit of the First Class:

Choose the smallest observation in the data set or a convenient number slightly lower than the smallest observation in the data set.

Determining the Class Width

Determine the class width by computing

Largest class number minus smallest class number divided by number of classes.

*round up to convenient number

Question 17

EXAMPLE Constructing a Frequency and Relative Frequency Histogram for Continuous Data

Answer 17

Question 18

What is a stem-and-leaf plot?

Answer 18

A stem-and-leaf plot uses digits to the left of the rightmost digit to form the stem. Each rightmost digit forms a leaf.

For example, a data value of 147 would have 14 as the stem and 7 as the leaf.

We let the stem represent the integer portion of the number and the leaf will be the decimal portion. For example, the stem of Alabama (2.8) will be 2 and the leaf will be 8

*Within each stem, rearrange the leaves in ascending order, title the plot, and include a legend to indicate what the values represent.*

Question 19

What does a split stem and leaf plot look like?

Answer 19

Question 20

What is an Advantage of Stem-and-Leaf Diagrams over Histograms?

Answer 20

Once a frequency distribution or histogram of continuous data is created, the raw data is lost (unless reported with the frequency distribution), however, the raw data can be retrieved from the stem-and-leaf plot.

Question 21

What is a dot plot?

Answer 21

A dot plot is drawn by placing each observation horizontally in increasing order and placing a dot above the observation each time it is observed.

EXAMPLE Drawing a Dot PlotThe following data represent the number of available cars in a household based on a random sample of 50 households. Draw a dot plot of the data.

3 0 1 2 1 1 1 2 0 2 4 2 2 2 1

2 2 0 2 4 1 1 3 2 4 1 2 1 2 2 3

Question 22

Identify the Shape of a Distribution

Uniform Distribution?

Bell-Shaped?

Skewed right?

Skewed Left?

Answer 22

Uniform distribution - the frequency of each value of the variable is evenly spread out across the values of the variable

Bell-shaped distribution - the highest frequency occurs in the middle and frequencies tail off to the left and right of the middle

Skewed right - the tail to the right of the peak is longer than the tail to the left of the peak

Skewed left - the tail to the left of the peak is longer than the tail to the right of the peak.

Question 23

What is a Time-Series Plot?

Answer 23

A time-series plot is obtained by plotting the time in which a variable is measured on the horizontal axis and the corresponding value of the variable on the vertical axis.

Line segments are then drawn connecting the points.

*If the value of a variable is measured at different points in time, the data are referred to as time series data

Question 24

What is descriptive statistics?

Answer 24

Descriptive statistics consists of organizing and summarizing data.

Question 25

What is **inferential statistics**?

Answer 25

**Inferential statistics** uses methods that take a result from a​ sample, extend it to the​ population, and measure the reliability of the result.

Question 26

What graph is common for representing **qualitative data**?

Answer 26

A b**ar graph**.

Question 27

When comparing data sets, what is best to use? Relative Frequencies or frequencies?

Answer 27

**When comparing** data sets, it is **best to use relative frequencies** because different sample or population sizes make comparisons using frequencies difficult or misleading.

Question 28

How do you **find the percentage for a sector of a pie chart?**

Answer 28

To find the percentage of a pie circle - **You must multiply the relative frequency by 360**. ## Footnote **Ex.** Relative frequency of 0.1091 x 360 = 39.2 percent.

Question 29

What is a **cumulative frequency**?

Answer 29

A **cumulative frequency** distribution displays the aggregate frequency of the category. In other words, it displays the total number of observations less than or equal to the upper class limit of the class. **Example:** So the cumulative frequency for the second class is the sum of the frequencies of classes 1 and 2; the cumulative frequency for the third class is the sum of the frequencies of classes 1,2, and 3; and so on.

Question 30

What is a **cumulative relative frequency?**

Answer 30

A **cumulative relative frequency** distribution displays the proportion (or percentage) of observations less than or equal to the upper class limit of the class. **Example looks like this**: *0.10* *\* to calculate add the relative frequencies in ascending form.*

Question 31

What does a c**umulative frequency and relatitive cumulative frequency** chart look like?

Answer 31

It is just the frequencies and relative frequencies added together in ascending form to find a cumulative. \*note relative frequencies are found by dividing the frequency by number of observations.

Question 32

What is an **ogive?** ## Footnote **How is a ogive constructed?**

Answer 32

An **ogive** (read as “oh jive”) is a graph that represents the cumulative frequency or cumulative relative frequency for the class. **How to:** A relative frequency ogive is drawn by plotting points whose x-coordinates are the upper class limit of each class and whose y-coordinates are the cumulative relative frequencies of each class. Then connect the points with line segments. Also, an additional line segment is drawn connecting the first point to the horizontal axis at a location representing the upper limit of the class that would precede the first class (if it existed).