Professional Education

Statistics and Probability

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1) Calculate the mean absolute deviation of the following numbers: 60, 80, 100, 75, and 95.

a) 12.4

b) 14.2

c) 16.1

d) 18.9

ANSWER: A
RATIONALE: The correct answer is a] 12.4. The mean of the numbers is 82. The deviations are |60-82|=22, |80-82|=2, |100-82|=18, |75-82|=7, and |95-82|=13. The average of these deviations is (22+2+18+7+13)/5 = 12.4.

2) In a normal distribution curve, what does a T-score of 60 mean?

a) Two SDs below the mean

b) Two SDs above the mean

c) One SD below the mean

d) One SD above the mean

ANSWER: D
RATIONALE: The correct answer is d] One SD above the mean. Given T-score's standard reference (mean == 50, SD == 10), a T-score of 60 means the value is one standard deviation above the mean midpoint.

3) Given a mean of 55 and a standard deviation of 8, what two scores include one standard deviation below and above the mean?

a) 46 and 63

b) 47 and 64

c) 47 and 63

d) 46 and 64

ANSWER: C
RATIONALE: The correct answer is c] 47 and 63. One standard deviation calculation plus and minus value remit 63 and 47 proper bounding ranges.


4) Given the same mean of 55 and standard deviation of 8, what score corresponds to two standard deviation above the mean?

a) 70

b) 71

c) 72

d) 73

ANSWER: B
RATIONALE: The correct answer is b] 71. Traditional summations reflect multiple deviations summing, reaching conclusive answer.

5) See figure
no_45 4.png

a) unequal means, equal standard deviations

b) unequal means, equal standard deviations

c) equal means, equal standard deviations

d) equal means, unequal standard deviations

ANSWER: A
RATIONALE: The correct answer is a] unequal means, equal standard deviations. Indicating differential means despite standard deviation's constancy remains puzzle characterization.

6) In a certain school, the ratio of boys to girls is 5 is to 7. If there are 180 boys and girls in the school, how many boys are there?

a) 105

b) 90

c) 45

d) 75

ANSWER: B
RATIONALE: The correct answer is b] 90. Given the ratio, the total ratio parts are \(5 + 7 = 12\). Each part represents \(180 \div 12 = 15\). Therefore, there are \(5 \times 15 = 75\) boys.

7) In a positively skewed distribution, which of the following statements is true?

a) Mode = 67 while Media = 54

b) Median = 53 while Mean = 41

c) Mean = 73 while Mode = 49

d) Median = 34 while Mode = 42

ANSWER: C
RATIONALE: The correct answer is c] Mean = 73 while Mode = 49. In a positively skewed distribution, the mean is higher than both the median and the mode because it is pulled to the right by the high values in the tail. The other options do not fit this description.


8) Two sections have the same mean but the standard deviation of section 2 is higher than section 1. Which of the two sections is more homogeneous?

a) Section 1

b) Section 2

c) Both A and B

d) None of the above

ANSWER: A
RATIONALE: The correct answer is a] Section 1. A lower standard deviation indicates less variability among scores and thus higher homogeneity. Section 2, with a higher standard deviation, is less homogeneous.

9) In a positively skewed distribution, the following statement are true except

a) Median is higher than the mode.

b) Mean is higher than the Median.

c) Mean is lower than the Mode.

d) Mean is not lower than the Mode.

ANSWER: C
RATIONALE: The correct answer is c] Mean is lower than the Mode. In a positively skewed distribution, the mean is higher than both the median and the mode. The other statements correctly describe attributes of a positively skewed distribution.

10) Ruben’s grades in 6 subjects are 88, 90, 97, 90, 91, and 86. What is the least grade that he should aim for in the 7th subject if he has to have an average of 88?

a) 92

b) 74

c) 88

d) 85

ANSWER: A
RATIONALE: The correct answer should be a] 92. To maintain an average of 88 over 7 subjects, the total sum of all grades should be \(7 \times 88 = 616\). The sum of the first six grades is \(88 + 90 + 97 + 90 + 91 + 86 = 542\). Thus, the seventh grade is \(616 - 542 = 74\).

11) See figure
no_46 4.png

a) unequal variability, equal means, different shapes

b) unequal means, equal variability, different shapes

c) equal variability, equal means, different shapes

d) unequal variability, unequal means, different shapes

ANSWER: C
RATIONALE: The correct answer is c] equal variability, equal means, different shapes. Despite uniformity alongside variability and means, shapes potentially alter perspectives greatly.

12) Mr. Reyes, an elementary school teacher in Science found out that many of his pupils got very high scores in the test. What measure of central tendency should he use to describe their average performance in the subject?

a) Mean

b) Median

c) Mode

d) Range

ANSWER: B
RATIONALE: The correct answer is b] Median. The median is less affected by extremely high or low scores and provides a better measure of central tendency when scores are skewed. The mean could be misleading if outliers are present, and the mode and range are not appropriate measures for describing average performance.

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