Examkin

Soru

Zorluk: ZorDescriptive Statistics and Data Representations

A technology company evaluated the annual performance scores of its employees across three departments: Marketing, Engineering, and Customer Support.

- The Marketing department has 2020 employees, with a mean performance score of 9292.
- The Engineering department has twice as many employees as the Marketing department, with a mean performance score of 8686.
- The Customer Support department has 1010 more employees than the Marketing department.
- The overall mean performance score across all employees in all three departments combined is 8484.

What is the mean performance score for the Customer Support department?

  1. A
    6060
  2. B
    7474
  3. 7676Cevap
  4. D
    7979
  5. E
    8484

Cevap

The mean performance score for the Customer Support department is 76.
To find the mean score for Customer Support, calculate the total points across all departments (90×84=7,56090 \times 84 = 7,560) and subtract the known total points from Marketing (20×92=1,84020 \times 92 = 1,840) and Engineering (40×86=3,44040 \times 86 = 3,440). The remaining 2,2802,280 points are divided by the 3030 Customer Support employees, yielding a mean of 7676.

Adım Adım Çözüm

1
Determine the number of employees in each department and the total employee count.
Marketing has 2020 employees. Engineering has 2×20=402 \times 20 = 40 employees. Customer Support has 20+10=3020 + 10 = 30 employees. Total employees = 20+40+30=9020 + 40 + 30 = 90.
Accurate employee counts per group are required to calculate weighted sums.
2
Calculate the total combined performance score for all 90 employees.
Total Score=90×84=7,560\text{Total Score} = 90 \times 84 = 7,560.
The sum of all individual scores is equal to the overall mean multiplied by the total number of employees.
3
Calculate the total performance scores for Marketing and Engineering.
Marketing total = 20×92=1,84020 \times 92 = 1,840. Engineering total = 40×86=3,44040 \times 86 = 3,440. Combined Marketing + Engineering total = 1,840+3,440=5,2801,840 + 3,440 = 5,280.
Each department's score contribution is its employee count multiplied by its mean score.
4
Subtract the Marketing and Engineering scores from the total combined score to find the Customer Support total score.
Customer Support total score = 7,560−5,280=2,2807,560 - 5,280 = 2,280.
The remaining score points belong to the Customer Support department.
5
Divide the Customer Support total score by the number of Customer Support employees.
Customer Support mean score = 2,28030=76\frac{2,280}{30} = 76.
The mean is the total department score divided by its employee count.

Anahtar Kavram

Weighted Mean and Subgroup Summaries
Bu soruyu puanla

Konular

Descriptive Statistics and Data Representations

Bu konudan daha fazla soru