Exercise: Average
Questions for: Calculation of Median/Standard Deviation
A small company tracks the number of projects completed by its team members each month. For the last month, the numbers reported by six team members were: 15, 18, 20, 22, 25, and 30. Later, it was discovered that one team member's report of 18 projects was an error, and the actual number was 28 projects.
What is the median number of projects completed by the team members after this correction?
A: 21
B: 22.5
C: 23.5
D: 24
Answer: C
1. First, update the data set with the corrected value: The original list was 15, 18, 20, 22, 25, 30. The value 18 is corrected to 28.
2. The new data set is: 15, 28, 20, 22, 25, 30.
3. To find the median, sort the data set in ascending order: 15, 20, 22, 25, 28, 30.
4. Since there is an even number of data points (6), the median is the average of the two middle values.
5. The two middle values are the 3rd and 4th terms in the sorted list, which are 22 and 25.
6. Calculate the average of these two values: (22 + 25) / 2 = 47 / 2 = 23.5.
Why others are wrong:
A — This is the median of the original, uncorrected data set.
B — This option results from an incorrect identification or averaging of the middle terms.
D — This option results from an incorrect calculation or misidentification of the middle terms.
Five colleagues, Alice, Bob, Carol, David, and Eve, each reported the number of books they read last month. Alice read 2 fewer books than Bob, who read 7. Carol read 1 more book than Alice. David read the same number of books as Bob. Eve read 3 books more than Carol.
What is the median number of books read by the colleagues last month?
A: 6
B: Eve read 3 books more than Carol.
What is the median number of books read by the colleagues last month?
A. 6
B. 7
C: 8
D: 9
Answer: B
1. Determine the number of books read by each colleague:
Bob = 7
Alice = Bob - 2 = 7 - 2 = 5
Carol = Alice + 1 = 5 + 1 = 6
David = Bob = 7
Eve = Carol + 3 = 6 + 3 = 9
2. List all the values: 5, 7, 6, 7, 9.
3. Arrange the values in ascending order: 5, 6, 7, 7, 9.
4. The median is the middle value in an ordered set of numbers.
5. In this set of five numbers, the middle value is 7.
Why others are wrong:
A — This is the number of books Carol read, not the median.
B — (Correct)
C — This is an incorrect calculation; possibly the mode if 7 occurred twice and was chosen without ordering.
D — This is the maximum number of books read (by Eve), not the median.
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A small business recorded its daily online sales in thousands of currency units for six days. The sales figures were: 12, 18, 15, X, 20, and 13. The median daily sales for these six days was 14.5 (thousand currency units).
What was the sales figure for the missing day (X)?
A: 13
B: 14
C: 15
D: 16
Answer: B
1. List the known sales figures in ascending order: 12, 13, 15, 18, 20.
2. There are 6 total sales figures (including X). For an even number of data points, the median is the average of the two middle values (the 3rd and 4th values when sorted).
3. The median is given as 14.5. Therefore, (3rd value + 4th value) / 2 = 14.5, which means the sum of the two middle values must be 29.
4. Let's place X = 14 into the sorted list: 12, 13, 14, 15, 18, 20.
5. In this sorted list, the 3rd value is 14 and the 4th value is 15.
6. The average of these two middle values is (14 + 15) / 2 = 29 / 2 = 14.5. This matches the given median.
Why others are wrong:
A — If X = 13, the sorted list is 12, 13, 13, 15, 18, 20. The median would be (13+15)/2 = 14.
C — If X = 15, the sorted list is 12, 13, 15, 15, 18, 20. The median would be (15+15)/2 = 15.
D — If X = 16, the sorted list is 12, 13, 15, 16, 18, 20. The median would be (15+16)/2 = 15.5.
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A small office monitors the daily number of email inquiries received over a week. The recorded numbers are 10, 18, 13, 50, 12, 16, and 15.
What is the median number of daily email inquiries?
A: 15
B: 19.14
C: 50
D: 10
Answer: A
1. Arrange the data points in ascending order: 10, 12, 13, 15, 16, 18, 50.
2. Count the number of data points (n). Here, n = 7.
3. For an odd number of data points, the median is the middle value.
4. The position of the median is (n+1)/2 = (7+1)/2 = 4th value.
5. The 4th value in the sorted list is 15.
Why others are wrong:
B — This is the approximate mean (average) of the data set.
C — This is the highest value in the data set.
D — This is the lowest value in the data set.
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A small bakery recorded the number of cakes sold each day over a period of seven days: 24, 30, 22, 28, 95, 25, 27. The owner wants to understand the typical daily sales figure, without it being skewed by unusual events or extreme values.
What is the median number of cakes sold daily for this period?
A: 27
B: 36
C: 22
D: 95
Answer: A
1. To find the median, the data set must first be arranged in ascending order.
2. The ordered data set is: 22, 24, 25, 27, 28, 30, 95.
3. There are 7 data points, which is an odd number.
4. The median is the middle value, found at the (n+1)/2 position.
5. For n=7, the position is (7+1)/2 = 4th.
6. The 4th value in the ordered set is 27.
Why others are wrong:
B — This is approximately the mean (average) of the data set, which is heavily influenced by the outlier (95).
C — This is the minimum value in the data set.
D — This is the maximum value (an outlier) in the data set.
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