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Updated on: 06 Mar 2026, 19:36
Originally posted by MartyMurray on 09 Dec 2025, 11:14.
Last edited by MartyMurray on 06 Mar 2026, 19:36, edited 2 times in total.
Last edited by MartyMurray on 06 Mar 2026, 19:36, edited 2 times in total.
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C
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Difficulty:
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67% (01:24) correct
33%
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wrong
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While researching the hourly frequency of a certain occurrence, researchers determined that the mean number of occurrences per hour was 18 and the standard deviation of the number of occurrences per hour was 5. However, later, they discovered that the number of occurrences each hour had been undercounted by 3. What was the sum of the correct mean and standard deviation of the number of occurrences per hour?
(A) 20
(B) 23
(C) 26
(D) 29
(E) Cannot be determined
Source: Marty Murray Coaching
(A) 20
(B) 23
(C) 26
(D) 29
(E) Cannot be determined
Source: Marty Murray Coaching
09 Dec 2025, 11:24
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While researching the hourly frequency of a certain occurrence, researchers determined that the mean number of occurrences per hour was 18 and the standard deviation of the number of occurrences per hour was 5. However, later, they discovered that the number of occurrences each hour had been undercounted by 3. What was the sum of the correct mean and standard deviation of the number of occurrences per hour?
so as the value are undercounted then there will be addition of 3 in value so the mean will be change by +3 so new mean will be 21 ,but the addition in value doesnot have any effect on SD so that will be same so SD will be 5
so sum of mean and SD will be 21+5=26
Answer is C
so as the value are undercounted then there will be addition of 3 in value so the mean will be change by +3 so new mean will be 21 ,but the addition in value doesnot have any effect on SD so that will be same so SD will be 5
so sum of mean and SD will be 21+5=26
Answer is C
12 Dec 2025, 08:17
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While researching the hourly frequency of a certain occurrence, researchers determined that the mean number of occurrences per hour was 18 and the standard deviation of the number of occurrences per hour was 5. However, later, they discovered that the number of occurrences each hour had been undercounted by 3. What was the sum of the correct mean and standard deviation of the number of occurrences per hour?
We see that "they discovered that the number of occurrences each hour had been undercounted by 3." So, the correct number of occurrences was 3 higher for every hour.
According, the correct mean was 3 higher than the mean first calculated.
So, the correct mean is 18 + 3 = 21.
The standard deviation of a set of values is basically the average distance of the values from the mean of the values.
When, 3 is added to every value in a set, the values all increase by 3, but the difference between each value and the mean remains the same.
For example, say we have the following values:
13, 13, 13, 23, 23, 23
The mean is 18, and the average distance from the mean is 5 since all of the values are 5 away from 18.
If we add 3 to every value, we get the following values:
16, 16, 16, 26, 26, 26
The new mean is 21, but the average distance from the mean remains 5.
So, the standard deviation has remained the same.
Standard deviation is calculated by means of a more complex process than is used above. At the same time, the basic principle remains the same: increasing all values by the same amount increases the mean but does not change the standard deviation.
So, in the case of this question, after the correction, the mean is 21, and the standard deviation is still 5.
21 + 5 = 26
(A) 20
(B) 23
(C) 26
(D) 29
(E) Cannot be determined
Correct answer: C
We see that "they discovered that the number of occurrences each hour had been undercounted by 3." So, the correct number of occurrences was 3 higher for every hour.
According, the correct mean was 3 higher than the mean first calculated.
So, the correct mean is 18 + 3 = 21.
The standard deviation of a set of values is basically the average distance of the values from the mean of the values.
When, 3 is added to every value in a set, the values all increase by 3, but the difference between each value and the mean remains the same.
For example, say we have the following values:
13, 13, 13, 23, 23, 23
The mean is 18, and the average distance from the mean is 5 since all of the values are 5 away from 18.
If we add 3 to every value, we get the following values:
16, 16, 16, 26, 26, 26
The new mean is 21, but the average distance from the mean remains 5.
So, the standard deviation has remained the same.
Standard deviation is calculated by means of a more complex process than is used above. At the same time, the basic principle remains the same: increasing all values by the same amount increases the mean but does not change the standard deviation.
So, in the case of this question, after the correction, the mean is 21, and the standard deviation is still 5.
21 + 5 = 26
(A) 20
(B) 23
(C) 26
(D) 29
(E) Cannot be determined
Correct answer: C
