Stats Quiz 3 - Tuesday 2/18/14

Question 1

What type of graph do you use for Nominal or Ordinal Data? How is it arranged and Why?

Answer 1

Bar graph where bars do not touch because there is no consistent numerical relation between the data.

In Nominal Data you can use any order.
For Ordinal Data you arrange smallest to largest.

Question 2

What type of graph(s) do you use for Interval or Ratio Data? How is it arranged and why?

Answer 2

The Histogram - one bar for each class interval; bars touch at the limits of the class intervals indicating the continuous nature of the data

The Frequency Polygon - Each dot represents the midpoint of the interval and the frequencies on the chart; Instead of bars, lines connect dots at the interval centers

Question 3

What are the different Shapes for Frequency Polygons?

Answer 3

At the midpoint (hump) in the graph:

Symmetrical - both sides of the graph are similar
vs.
Skewed - both sides of the graph look very different

Question 4

What are the Different shapes of a Symmetrical Frequency Polygon?

Answer 4

Bell Shaped
Rectangular/Uniform
U Shaped

Question 5

What are the Different tails of a Skewed Freq. Polygon?

Answer 5

Negatively Skewed - tail pointed to the right
Positively Skewed - tail pointed to the left
J Shaped - positive or negative skew with no “hump”

Positive and negative skew is talked about in terms of where the scores are, where the tail is NOT where the hump is

Tip: When reflected over the x-axis, where does the arrow point?

Question 6

What is Central Tendency?

Answer 6

a measure of what the middle of a distribution of scores is:

where do the scores cluster?
what is the average score?

Question 7

What is Variability?

Answer 7

how much the scores in a distribution differ from each other (how tightly packed they are around the middle):

Are they all very close to the central tendency?
Are they very spread out?

Question 8

What are the Three Measures of Central Tendency?

Answer 8

Mode - the most frequent occurring score in the data (most)

Median - the 50th percentile that splits the scores in half (middle)

Mean - the average of all the scores in the data (average)

Question 9

What is the MODE?

Answer 9

Which of the scores occurs the most frequently? Just count up and tally up the freq, of the scores

Nominal data is typically described using Mode
Can be used to describe Ordinal, Interval and Ratio

Can be easily assessed using a Bar Graph

Question 10

What is Uni-Modal vs. Bi-Modal vs. No Mode?

Answer 10

Uni-Modal - shows one clear winner
Bi-Modal - two equal or almost equal humps in the data
No-Mode - More than two modes… eg. tri-modal or with all other values at 0

Question 11

How do you determine the Mode using Ordinal, Interval or Ratio Data in a Frequency Polygon?

Answer 11

The highest “hump” in the line graph determines the mode; can state whether the frequency distribution is positively or negatively uni-modal, bi-modal or no-modal…

Question 12

What is the MEDIAN?

Answer 12

The score which splits the distribution in half with a set of RANKED-SCORES (in order). Must use ORDINAL, INTERVAL, or RATIO data

Question 13

How do you determine the Median using ungrouped data?

Answer 13

Order the data

• If the number of scores is odd, the median is the score in the middle
• If the number of scores is even, the median is the average of the two scores in the middle

Question 14

How do you determine the Median using grouped data?

Answer 14

Using the Percentile Point Formula

KNOW HOW TO USE THIS FORMULA

Question 15

Which is the preferred measure of central tendency for Ordinal Data?

Answer 15

Median

Question 16

How do you compute the Mean?

Answer 16

Mean = Average

Sum up all the scores and divide by the number of scores in the distribution

Question 17

True or False: Mean can be used for Ordinal Data

Answer 17

FALSE

Mean is typically used for Interval and Ratio Data

Question 18

True or False: Mean is typically used for Interval and Ratio Data

Answer 18

TRUE - you cannot use the mean to find Nominal Data or with Ordinal Data, “rank” orderings are not “summable”

E.g. XS – SM – MD – LG – XL
You cannot sum up Lg + XL

E.g. you cannot say that the average of a size 7 dress and a size 9 dress is a size 8 dress

Question 19

How do you calculate the Deviation?

Answer 19

Deviation = Xi - M

• The sum of the deviations about the mean is zero
• A deviation is the distance each original score is from the mean

Question 20

What can we determine looking at a Frequency Polygon if the Distribution is Symmetrical and Unimodal?

Answer 20

Mean, Median and Mode ARE Equal

Question 21

What can we determine looking at a Frequency Polygon if the Distribution is Skewed?

Answer 21

Mean, Median and Mode are NOT Equal

The MEAN always gets pulled into the tail:
• if mean is larger than mode; it’s positively skewed
• if mean is less than mode; it’s negatively skewed

Question 22

What can we determine looking at a Frequency Polygon if the Distribution is Negatively Skewed?

Answer 22

Mean < Mode

Question 23

What can we determine looking at a Frequency Polygon if the Distribution is Positively Skewed?

Answer 23

Mean > Mode

Question 24

What is Nominal Data?

Answer 24

a scale of names; labeling it or putting it into categories

data is Qualitative (there is no magnitude)

Question 25

What is Ordinal Data?

Answer 25

can be measured and put in order from smallest to largest. Ordinal data does NOT have equal intervals.

Ordinal Data has MAGNITUDE (know whether one score is more, less or equal to another); however the distance between each score is NOT equal

E.g. The racers can be ordered 1st, 2nd, 3rd, 4th… BUT, this difference in finishing time between 1st and 2nd is not necessarily the same as the difference in finishing time between 3rd and 4th

Question 26

What is Interval Data?

Answer 26

the gaps are consistent throughout with equal intervals; We can rank order the data and we know that the difference between any two places is equivalent

Interval Data has MAGNITUDE AND EQUAL INTERVALS (distance between each score IS equal)

E.g.The temperature (°F ) at which coffee is served is interval data

• If I add an equal amount of heat to a cup of coffee at 51°F and a cup of coffee at 80 °F the temperature reading of each cup will change by an identical amount
• A degree is the same size throughout the scale
• The difference between 51°F and 52 °F is 1°F
• The difference between 80°F and 81°F is 1°F

Question 27

What is Ratio Data?

Answer 27

Ratio Data has MAGNITUDE, EQUAL INTERVALS, and an ABSOLUTE ZERO POINT

• We can rank order the data and we know that the difference between any two places is equivalent, we can have none of the variable

E.g. Temperature in Kelvin is ratio data

• Zero degrees Kelvin is the point where there is no heat, zero is the bottom of the scale where (at 0 Kelvin molecules stop moving)
• Zero degrees on the Fahrenheit or Celsius scale does not mean there is NO heat.