Statistics Demystified, 2nd edition |

Stan Gibilisco |

Explanations for Quiz Answers in Chapter 2 |

1. Statisticians define a discrete variable as a quantity that
can attain only certain, well-defined values corresponding to points on
a number line, such as all the positive whole numbers less than 500.
The correct choice is B. |

2. In a discrete distribution, the mode is the value that the
discrete variable attains with the greatest frequency. The correct choice
is B. Some discrete distributions have more than one mode; we call them
multimodal distributions. In a discrete distribution where each
value of the discrete variable occurs exactly as often as all the other
values do, we say that the distribution has no mode, or that the mode is
undefined. |

3. In order to determine the mean score 0 + 1 + 2 + 3 + ... + 18 + 19 + 20 = 210 Then we divide by the number of values (in this case 21), getting a mean score of
The correct choice is D. |

4. As defined at the bottom of page 59, the term measure of central tendency
refers to either the mean, the median, or the mode. Based on that strict
and straightforward standard, the answer is clearly A. |

5. As defined in the "Tip" on page 62, variance
and standard deviation both constitute measures of dispersion.
Based on that rigid criterion, the correct choice is D. |

6. In a discrete distribution, we define the
If we choose values one by one and test them for adherence to this definition, we'll find that the median must be 18. We have 19 elements less than or equal to 18, which we can denote as the set
and 19 elements greater than or equal to 18, which we can portray as the set
The correct choice is C. |

7. In this situation, the only two scores that got any "hits" are 8 correct and 10 correct. Both of these scores occurred with the same frequency, so they both represent modes (we have a bimodal distribution). The correct choice is A. |

8. Recall the definition of the term median as it applies to a discrete
distribution. It's the value (or the average of two competing values) such that
the number of elements greater than or equal to it is the same as the number of elements
less than or equal to it. In this case, that's the score of 9 (even though no one
actually got that score). The correct choice is B. |

9. Before we can calculate the variance, we must know the mean score
expressed to three decimal places. If we call our discrete variable Var ( µ)^{2}]where x) = 1.000 carried
out to three decimal places. We can intuitively see
that this figure makes sense when we recall the fact that in a discrete
distribution, the variance equals the average of the squares of the "distances"
of each value from the mean. All the scores in this distribution lie either "1 below
the mean" or else "1 above the mean," and we observe an equal number
of lower scores and higher scores. The correct choice is C. |

10. By definition, the standard deviation equals the square root of
the variance. We've calculated the variance as exactly equal to 1 (or 1.000,
carried out to three decimal places). Therefore, the standard deviation also
equals 1.000 (carried out to three decimal places). The answer is C. |