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Difficulty: MediumDescriptive Statistics and Data Representations

A store manager records the number of laptop computers sold each day during a 5-day work week. The daily sales, in chronological order from Monday to Friday, are 2, 10, 9, 4, and 5. What is the positive difference between the mean and the median of the number of laptops sold daily?

  1. A
    3
  2. 1Answer
  3. C
    4
  4. D
    17
  5. E
    21

Answer

The positive difference between the mean and the median of the daily laptop sales is 1.
To find the correct answer, we first calculate the mean of the dataset by summing the numbers (2+10+9+4+5=302 + 10 + 9 + 4 + 5 = 30) and dividing by the count (30/5=630 / 5 = 6). Next, we find the median by sorting the dataset (2,4,5,9,102, 4, 5, 9, 10) and selecting the middle value, which is 55. The positive difference between the mean and the median is 6−5=16 - 5 = 1.

Step-by-Step Solution

1
Calculate the mean of the daily laptop sales.
The sum of the laptop sales is 2+10+9+4+5=302 + 10 + 9 + 4 + 5 = 30. Since there are 5 days, the mean is 305=6\frac{30}{5} = 6.
The mean is calculated by dividing the sum of all values by the total number of values.
2
Find the median of the daily laptop sales.
Sorting the sales in ascending order gives 2,4,5,9,102, 4, 5, 9, 10. The middle value (the 3rd number) is 55.
The median of a set of numbers is the middle value when the numbers are arranged in order.
3
Calculate the positive difference between the mean and the median.
The positive difference is 6−5=16 - 5 = 1.
Subtract the smaller value from the larger value to find the positive difference.

Key Concept

Calculating and comparing descriptive statistics (mean and median) of a dataset.
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Topics

Descriptive Statistics and Data Representations

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