Answers to the Statistics Quiz

Answers to the Statistics Quiz

1. Find the mode of the following data:
15, 19, 17, 20, 25, 19, 17, 22, 17

(1) 17
(2) 19
(3) 22
(4) 25

Ans: (1) 17
Since the question asks for the mode, which means the most often number in the set of data, one should look at the number of times each number appear:

Number	Frequency
15	1
17	3
19	2
20	1
22	1
25	1

As we can see from the table above, since the number 17 appears three times, which is the most often, the answer to the question should be choice (1).

2. If the height of four tennis players are 172 cm, 166 cm, 162 cm, and 172 cm, what is the median height of these tennis players?

(1) 166 cm
(2) 168 cm
(3) 169 cm
(4) 172 cm

Ans: (3) 169 cm
Since the question asks for the median, which is the middle number, one should first arrange the data in increasing order:
162, 166, 172, 172
Note that there are four (an even) number in the set, thus, the median should be the average of the middle two numbers, in this case, take the average of 166 and 172. (166+172) / 2 = 338 / 2 = 169. Therefore, the answer to the question should be choice (3 ).

3. Express, in terms of x, the mean of 2x+4 and 6x-8.

(1) 2x + 4
(2) 4x - 2
(3) 6x - 8
(4) 8x - 4

Ans: (2) 4x - 2
Since the question ask for the mean of two numbers, one should add up the two numbers, and then divide the sum by 2. (2x+4) + (6x-8) = 8x-4, divide 8x-4 by 2, (8x-4)/2 = 4x-2. Therefore, the answer to the question should be choice (2).

4. For the data 7, 7, 9, 10, 17, which of the following statement is true?

(1) mean = median
(2) median = mode
(3) mean > mode
(4) mean < mode

Ans: (3) mean > mode
Since the question ask us to compare the mean, the median, and the mode, we should find these numbers first.
mean = (7+7+9+10+17) / 5 = 10
median = 9 (the middle number)
mode = 7 (since 7 appear twice, while the other numbers only appeared once).
As we can see, choice c is the only correct answer among the choices given to us. Clearly the mean, 10, is greater than the mode, which is only 7. Therefore, the answer to the question should be choice (3).

5. Susan received 82, 89, and 78 on the first three tests in her Statistics class. What is the lowest score that she must receive on her next test in order to have at least an average of 85 in the class?

(1) at least 78
(2) at least 82
(3) at least 89
(4) at least 91

Ans: (4) at least 91
Since the question asks us the average score of the four tests, one should realize that the mean is being asked for, and thus, we should add up the four test scores and divide that by 4. However, we do not know what score Susan is going to get in her four test. One way to get around this is to let the four test score be x. Ha, we are back to algebraic expression!
(82+89+78+x) / 4 = 85; (249+x) / 4 = 85; 249 + x = 340.
Solve for x and you will see that x = 91. In other words, Susan needs to get a 91 on her last test in order to get an average of 85 in the class. Therefore, the correct answer to the question should be choice (4).

6. In the set of scores below, how many scores are less than the median? 69, 50, 62, 42, 52

(1) 1
(2) 2
(3) 3
(4) 4

Ans: (2) 2
Since the question asks us the median, we should realize that median means middle. The first thing is to arrange the data in increasing order.
42, 50, 52, 62, 69
Now, since there are 5 test scores in the set, the middle number is the third number, which happens to be 52. But the question ask us how many scores are below 52. Just look at the set and you will notice that 2 of the scores are below and 2 of them are a bove. Therefore, the answer to the question should be choice (2).

7. Find the mean of the following numbers:
0.35, 0.5, 1/4, 0.75, 3/5, 0.25

(1) 0.25
(2) 0.35
(3) 0.45
(4) 0.50

Ans: (3) 0.45
Since the question asks us about the mean, we should add all of the data and divide that by the total number of values in the set.
(0.35+0.5+0.25+0.75+0.6+0.25) / 6 = 2.70 / 6 = 0.45
Therefore, the answer to the question should be choice (3).

8. Five girls in a JV volleyball team reported the number of boxes of candies that they sold in an academic year:
30, 30, 50, 60, 80. Which of the following is true?

(1) The median is equal to the mode
(2) The mean is 20
(3) The median is 20
(4) The mean is equal to the median

Ans: (4) The mean is equal to the median.
Since the question ask us to compare the mean, the median, and the mode, we should find these numbers first.
mean = (30+30+50+60+80) / 5 = 50
median = 50 (the middle number)
mode = 30 (since 30 appear twice, while the other numbers only appeared once).
As we can see, choice d is the only correct answer among the choices given to us. Clearly the mean, 50, is equal to the median, which is also 50. Therefore, the answer to the question should be choice (4).

9. For which set of data do the mean, median, and mode all have the same value?

(1) 7, 9, 9, 9, 11
(2) 7, 7, 8, 11, 12
(3) 7, 7, 7, 8, 11
(4) 7, 7, 9, 11, 16

Ans: (1) 7,9,9,9,11
Since the question ask us to compare the four sets of data, it is necessary for us to find the mean, the median, and the mode for each of them

for (1) 7,9,9,9,11
mean = (7+9+9+9+11) / 5 = 9
median = 9
mode = 9
Aha, this happens to be the right choice. But we should test the remaining choices to make sure that there is only one correct answer.

for (2) 7,7,8,11,12
mean = (7+7+8+11+12) / 5 = 9
median = 8
mode = 7

for (3) 7,7,7,8,11
mean = (7+7+7+8+11) / 5 = 8
median = 7
mode = 7

for (4) 7,7,9,11,16
mean = (7+7+9+11+16) / 5 = 10
median = 9
mode = 7

As we can see, the correct answer to the question is choice (1).

10. A number is selected at random from the set 2,2,2,2,3,3,3,7. Find the probability that the number selected is the mode.

(1) 0
(2) 1/8
(3) 3/8
(4) 4/8

Ans: (4) 4/8
First of all, the question asks us about mode, which is the most often appeared number, in our question, this is 2, since it appears four times. In order to answer this question, we need to know a little about probability. The probability of selecting the mode is equal the number of ways in which we will get a success (in this case, the mode = 2), over the number of ways we can pick a number from the set (since we have 8 numbers, there's 8 ways). Therefore, the probability is 4/8, or choice (4).

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