Q. In a data set, the values are: 1, 2, 3, 4, 5. What is the interquartile range?
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Solution
Q1 = 2, Q3 = 4. Interquartile Range = Q3 - Q1 = 4 - 2 = 2.
Correct Answer: B — 2
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Q. In a deck of 52 cards, what is the probability of drawing a heart given that the card drawn is a red card?
A.
1/2
B.
1/4
C.
1/3
D.
1/5
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Solution
There are 26 red cards (hearts and diamonds). The number of hearts is 13. Thus, P(Heart | Red) = 13/26 = 1/2.
Correct Answer: A — 1/2
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Q. In a deck of cards, what is the probability of drawing a heart given that the card drawn is a red card?
A.
1/2
B.
1/4
C.
1/3
D.
1/5
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Solution
There are 26 red cards (hearts and diamonds). The number of hearts is 13. Thus, P(Heart | Red) = 13/26 = 1/2.
Correct Answer: A — 1/2
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Q. In a family of 4 children, what is the probability that at least one is a girl given that there are at least 2 boys?
A.
1/2
B.
3/4
C.
1/4
D.
2/3
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Solution
If there are at least 2 boys, the possible combinations are (2B, 2G), (3B, 1G), (4B). Thus, the probability of having at least one girl is 3/4.
Correct Answer: B — 3/4
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Q. In a family with 3 children, what is the probability that at least one child is a girl given that at least one child is a boy?
A.
0.75
B.
0.5
C.
0.25
D.
0.6
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Solution
The total outcomes for 3 children are 8. The outcomes with at least one boy are 7. The outcomes with at least one girl and one boy are 6. Thus, P(Girl|Boy) = 6/7 ≈ 0.857.
Correct Answer: A — 0.75
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Q. In a frequency distribution, if the class intervals are 0-10, 10-20, 20-30 and their frequencies are 5, 10, 15 respectively, what is the mode?
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Solution
The modal class is 20-30 as it has the highest frequency (15).
Correct Answer: C — 20
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Q. In a frequency distribution, if the class intervals are 0-10, 10-20, 20-30 and their frequencies are 5, 10, 15, what is the mode?
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Solution
Mode is the class with the highest frequency, which is 20-30.
Correct Answer: B — 20
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Q. In a frequency distribution, if the class intervals are 0-10, 10-20, 20-30, and the frequencies are 5, 10, 15 respectively, what is the mode?
A.
10
B.
20
C.
30
D.
None of the above
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Solution
The modal class is 20-30 since it has the highest frequency.
Correct Answer: B — 20
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Q. In a frequency distribution, if the class intervals are 0-10, 10-20, and 20-30 with frequencies 5, 10, and 15 respectively, what is the mode?
A.
10
B.
20
C.
30
D.
No mode
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Solution
The modal class is 20-30 since it has the highest frequency (15).
Correct Answer: B — 20
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Q. In a frequency distribution, if the mode is 10 and appears 15 times, what can be said about the data?
A.
It is uniform
B.
It is bimodal
C.
It is unimodal
D.
It is multimodal
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Solution
Since there is one mode (10), the data is unimodal.
Correct Answer: C — It is unimodal
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Q. In a frequency distribution, if the mode is 10 and the highest frequency is 15, what can be said about the data?
A.
It is uniform
B.
It is bimodal
C.
It is unimodal
D.
It is multimodal
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Solution
Since there is one mode (10), the data is unimodal.
Correct Answer: C — It is unimodal
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Q. In a frequency distribution, if the mode is 10 and the highest frequency is 5, what can be said about the data?
A.
It is uniform
B.
It is bimodal
C.
It is unimodal
D.
It is multimodal
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Solution
Since there is one mode (10), the data is unimodal.
Correct Answer: C — It is unimodal
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Q. In a frequency distribution, if the mode is 12 and the frequency of 12 is 10, what can be inferred about the data?
A.
Data is uniform
B.
Data is skewed
C.
Data has multiple modes
D.
Data is bimodal
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Solution
A single mode indicates that the data is likely skewed.
Correct Answer: B — Data is skewed
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Q. In a geometric series, if the first term is 4 and the common ratio is 3, what is the 4th term?
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Solution
The nth term of a geometric series is given by a_n = ar^(n-1). Thus, a_4 = 4 * 3^(4-1) = 4 * 27 = 108.
Correct Answer: A — 108
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Q. In a group of 100 people, 60 like cricket, 30 like football, and 10 like both. What is the probability that a person likes football given that they like cricket?
A.
1/6
B.
1/3
C.
1/2
D.
1/4
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Solution
P(Football|Cricket) = P(Football and Cricket) / P(Cricket) = 10/60 = 1/6.
Correct Answer: A — 1/6
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Q. In a group of 100 people, 60 like football, 30 like basketball, and 10 like both. What is the probability that a person likes football given that they like basketball?
A.
0.5
B.
0.3
C.
0.6
D.
0.7
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Solution
Using conditional probability, P(Football | Basketball) = P(Football and Basketball) / P(Basketball) = 10/30 = 1/3.
Correct Answer: C — 0.6
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Q. In a group of 50 people, 20 are smokers and 30 are non-smokers. If a person is selected at random, what is the probability that the person is a non-smoker given that they are not a smoker?
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Solution
If the person is not a smoker, they must be a non-smoker. Therefore, the probability is 1.
Correct Answer: A — 1
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Q. In a group of 50 people, 30 like tea, 20 like coffee, and 10 like both. What is the probability that a randomly selected person likes either tea or coffee?
A.
0.4
B.
0.6
C.
0.5
D.
0.7
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Solution
Using the principle of inclusion-exclusion, the number of people who like either tea or coffee is 30 + 20 - 10 = 40. The probability is 40/50 = 0.8.
Correct Answer: B — 0.6
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Q. In a lottery, 10 tickets are sold. If you buy 1 ticket, what is the probability of winning?
A.
1/10
B.
1/5
C.
1/2
D.
1/20
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Solution
There is 1 winning ticket out of 10. Probability = 1/10.
Correct Answer: A — 1/10
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Q. In a lottery, there are 10 tickets, and 3 of them are winning tickets. If one ticket is drawn at random, what is the probability that it is a winning ticket?
A.
1/10
B.
1/3
C.
3/10
D.
7/10
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Solution
The probability of drawing a winning ticket is 3/10.
Correct Answer: C — 3/10
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Q. In a lottery, there are 10 tickets, and 3 of them are winning tickets. What is the probability of selecting a winning ticket?
A.
1/10
B.
3/10
C.
1/3
D.
1/5
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Solution
The probability of selecting a winning ticket is the number of winning tickets divided by the total number of tickets, which is 3/10.
Correct Answer: B — 3/10
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Q. In a lottery, there are 10 tickets, of which 2 are winning tickets. What is the probability of selecting a winning ticket?
A.
1/5
B.
1/10
C.
1/2
D.
2/10
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Solution
The probability of selecting a winning ticket is the number of winning tickets divided by the total number of tickets, which is 2/10 = 1/5.
Correct Answer: B — 1/10
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Q. In a lottery, there are 10 tickets, of which 3 are winning tickets. What is the probability of selecting a winning ticket?
A.
1/10
B.
1/3
C.
3/10
D.
7/10
Show solution
Solution
The probability of selecting a winning ticket is the number of winning tickets divided by the total number of tickets, which is 3/10.
Correct Answer: C — 3/10
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Q. In a lottery, there are 100 tickets, and 10 of them are winning tickets. If one ticket is drawn at random, what is the probability that it is a winning ticket?
A.
1/10
B.
1/5
C.
1/20
D.
1/50
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Solution
The probability of drawing a winning ticket = Number of winning tickets / Total tickets = 10/100 = 1/10.
Correct Answer: A — 1/10
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Q. In a lottery, there are 100 tickets, and 10 of them are winning tickets. What is the probability of selecting a winning ticket?
A.
1/10
B.
1/5
C.
1/20
D.
1/50
Show solution
Solution
The probability of selecting a winning ticket is the number of winning tickets divided by the total number of tickets, which is 10/100 = 1/10.
Correct Answer: A — 1/10
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Q. In a normal distribution, approximately what percentage of data lies within one standard deviation of the mean?
A.
50%
B.
68%
C.
75%
D.
95%
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Solution
In a normal distribution, approximately 68% of the data lies within one standard deviation of the mean.
Correct Answer: B — 68%
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Q. In a normal distribution, what percentage of data lies within one standard deviation from the mean?
A.
68%
B.
95%
C.
99%
D.
50%
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Solution
In a normal distribution, approximately 68% of the data lies within one standard deviation from the mean.
Correct Answer: A — 68%
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Q. In a normal distribution, what percentage of data lies within one standard deviation of the mean?
A.
50%
B.
68%
C.
75%
D.
95%
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Solution
In a normal distribution, approximately 68% of the data lies within one standard deviation of the mean.
Correct Answer: B — 68%
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Q. In a sequence defined by a_n = 2^n, what is the 5th term?
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Solution
a_5 = 2^5 = 32.
Correct Answer: A — 16
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Q. In a sequence defined by a_n = 2^n, what is the value of a_5?
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Solution
a_5 = 2^5 = 32.
Correct Answer: A — 32
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