Chapter 3: Graphical Descriptive Techniques II

Question 1

Classes

Answer 1

Sets of intervals that together cover the complete range of observation

• no overlap
• not essentially they be equally wide but it does make analysis easier

Question 2

Histogram

Answer 2

Bar graph where bases of bars are the intervals and heights are frequencies

Good for for showing frequency distribution

Use excel data analysis function
- Excel counts numbers that are greater than lower limit and less than or equal to upper limit

Question 3

Determining number of class intervals

Answer 3

Depends on number of observations in data set

Sturges’ formula:
For n observations, number of class intervals = 1+ (3.3*log(n))
Round up

Observations
<50 : 5-7 classes
50-200 : 7-9 classes
200-500 : 9-10 classes
500-1000 : 10-11 classes
1000-5000 : 11-13 classes
5000-50000 : 13-17 classes
>50,000 : 17-20 classes

Question 4

To determine approximate class interval width

Answer 4

Width = (largest observation - smallest observation) / number of classes

Round to convenient value

Then define lower limit for first class from which all other limits will be determined (first class interval must contain smallest observation)

Consider ease of interpretation!! Exceptions apply if guidelines will not yield a histogram that is easy to interpret

Question 5

Histogram shape: symmetrical

Answer 5

If, when a vertical line is drawn down the center of a histogram the two sides are identical in shape and size

Question 6

Histogram shape: skewness

Answer 6

A histogram with a long tail extending in one direction (tail = fewer occurances)

Extending to the right: positively skewed
Extending to the left: negatively skewed

Question 7

Mode

Answer 7

Observation which occurs with the greatest frequency

Question 8

Modal class

Answer 8

The class in a histogram (frequency table) with the largest number of observations

Question 9

Histogram shape: unimodal

Answer 9

A histogram with a single peak (one class contains the most data)

Question 10

Histogram shape: bimodal

Answer 10

A histogram with two peaks. (Peaks do not have to be of equal hight)

Often indicate that two different distributions are present

Question 11

Histogram shape: Bell

Answer 11

Symmetric, unimodal histogram

Question 12

Return on investment

Answer 12

= gain (or loss)/ value of investment

Question 13

Modal class

Answer 13

Class that contains the greatest frequency of observations

Question 14

Factors that identify when to use a histogram

Answer 14

Objective is to describe a single set of data

Data type: interval

Question 15

Cross-sectional data

Answer 15

Observations are measured at the same time

Question 16

Time-series data

Answer 16

Observations are measurements at successive points in time

Data may be interval (Quantitative values) or nominal (frequency of value)

Question 17

Line chart

Answer 17

Often used to graphically depict time-series data

Plots a values of a variable (vertical axis) over time (horizontal axis)

Question 18

CPI

Answer 18

Basket at current year prices / basket at base year prices x 100

Question 19

To remove the effect of inflation

Answer 19

Divide current prices by current cpi and then multiply by 100

Shows relative base- year price

Question 20

Scatter diagram

Answer 20

Technique to describe the relationship between two variables

When one is dependent:
Y axis = dependent variable
X axis = independent variable

Otherwise which variable is on which axis is arbitrary

Most important characteristics are strength and direction of the linear relationship

Question 21

Linearity

Answer 21

How closely the scattered data adheres to a linear line.
Can be:
strong (points are close to a line)
medium-strength
weak (points appear to be scattered randomly)

Least squares method used to objectively choose the linear line used

(Relationships might also be quadratic or exponential)

JUST BECAUSE VARIABLES HAVE LINEAR RELATIONSHIP DOES NOT MEAN THERE’S A CAUSAL RELATIONSHIP.

Correlation =/= causation

Question 22

Positive linear relationship

Answer 22

One variable increases as the other increases (variables trend in the same direction)

Question 23

Negative linear relationship

Answer 23

One variable decreases as the other increases (variables trend in opposite directions)

Question 24

Factors that identify when to use a scatter diagram

Answer 24

When the objective is to describe a relationship between two variables

With interval-type data