Question 1

Give two differences between continuous and discrete scales.

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Question 2

If the quantity ΣX = 400.3 for N observations, then the quantity ΣX will equal 40.03 if each of the original observations is multiplied by 0.1.

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This is true because if each observation is multiplied by 0.1, then their sum will be 0.1 times the original sum. So, ΣX will be 400.3 x 0.1 = 40.03.

Question 3

Define discrete variable.

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Question 4

Prove algebraically that  .

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Question 5

Rounding 55.55 to the nearest whole number gives 55.

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Rounding 55.55 to the nearest whole number gives 56, because when the first decimal place is 5 or more, you round up.

Question 6

What are the four types of scales and what mathematical operations can be done with each?

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Question 7

Define continuous variable.

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Question 8

One generally has to specify the real limits for discrete variables since they cannot be measured accurately.

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Discrete variables are countable in a finite amount of time and do not require specifying real limits for measurement accuracy, unlike continuous variables which can take any value within a range and may require specifying limits for practical measurement.

Question 9

What is a discrete variable? Give an example.

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Question 10

Define real limits of a continuous variable.

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Question 11

Define interval scale.

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Question 12

When a weight is measured to 1/1000th of a gram, that measure is absolutely accurate.

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No measurement is absolutely accurate. When a weight is measured to 1/1000th of a gram, there may still be small errors or variations in the measuring instrument or the environment.

Question 13

Define nominal scale.

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Question 14

The faculty of a psychology department are trying to decide between three candidates for a single faculty position. The department chairperson suggests that to decide, each faculty person should rank order the candidates from 1 to 3, and the ranks would then be averaged. The candidate with the highest average would be offered the position. Mathematically, what is wrong with that proposal.

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Question 15

Define ratio scale.

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Question 16

The average number of children in a classroom is an example of a discrete variable.

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The average number of children in a classroom is not a discrete variable, as it can take on a range of values that are not necessarily whole numbers. It is a continuous variable.

Question 17

Student A claims that because his IQ is twice that of Student B, he is twice as smart as Student B. Is student A correct? Explain.

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Question 18

The symbol S means square the following numbers and sum them.

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The symbol "S" does not universally mean to square numbers and sum them; its meaning depends on the context in which it is used.

Question 19

How does an interval scale differ from an ordinal scale?

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Question 20

What is meant by "the real limits of a continuous variable."

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Quiz 2: Basic Mathematical and Measurement Concepts