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Week 2 assignment:

12. Explain and give an example for each of the following types of variables: (a) equal-

interval, (b) rank-order, (c) nominal, (d) ratio scale (e) continuous.

(a) equal-interval: This scale has equal interval hence we can perform differences but does not

have an absolute zero so we cannot perform division on these variables. These satisfaction levels

of visitors (on Likert scale) on a scale of 1 to 5 this scale lies between rank order and ratio scale.

(b) rank-order: These variables are in the next stage from the nominal. We can arrange them in

rank order but cannot do any other statistical operation such as difference, multiplication or

division. The education level:  elementary school, high school, some college, and college

graduate.

(c) Nominal: We cannot perform any static operations on these variables. Gender: Male &

Female

(d) ratio scale: This scale has an absolute zero and we can perform all possible statistical

operations on these variables. Like addition, difference, multiplication and division. Example:

Temperature in Kelvin or age

(e) continuous: These variables have all possible values within the given range. For example

weight or age. We can measure age on all possible points on the number line say between 0 to

100 years.

15. Following are the speeds of 40 cars clocked by radar on a particular road in a 35-mph

zone on a particular afternoon: 30, 36, 42, 36, 30, 52, 36, 34, 36, 33, 30, 32, 35, 32, 37, 34, 36,

31, 35, 20, 24, 46, 23, 31, 32, 45, 34, 37, 28, 40, 34, 38, 40, 52, 31, 33, 15, 27, 36, 40

Make (a) a frequency table and (b) a histogram, then (c) describe the general shape of the

distribution.

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The lowest value is 15 and highest value is 52, thus we make 7 classes with CI of 6

Frequency Table

CI Frequency

12-17 1

18-23 2

24-29 3

30-35 16

36-41 11

42-47 3

48-53 2

Total 38

Histogram

12-17 18-23 24-29 30-35 36-41 42-47 48-53024681012141618

Speed of Cars

Class Interval

Fre

qu

ency

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19 Give an example of something having these distribution shapes: (a) bimodal, (b)

approximately rectangular, and (c) positively skewed. Do not use an example given in this

book or in class.

(a) Bimodal: Distribution of height of people in a company (with both males and females - males

and females will have one mode each creating bi-modal distribution).

(b) Approximately rectangular: In this each value the variable can take has an equal

probability. Distribution of heads and tails in a large numbers of coin tosses, or distribution of

outcome of a dice throw.

(c) Positively skewed: Marks obtained in a very tough stats exams. A large number of students

will have low scores with few exceptional students scoring high or even 100%.

20. Find an example in a newspaper or magazine of a graph that misleads by failing to use

equal interval sizes or by exaggerating proportion.

The graph is misleading as Y axis is chosen to overemphasis the differences, while the actual

differences are not that much. (Please see the Excel graph in the second attachment for more

details).

P.S: Scroll down for the newspaper.

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