Team Performance: Mean & Standard Deviation
Calculate the mean and standard deviation for both Heritage Foods sales teams. Which team shows more consistent performance in distributing dairy products to major supermarket chains like More, Ratnadeep, and Q-Mart?
Related Concepts
Hint
Calculate the average sales for each team. Then, for standard deviation, find how much each month's sales deviate from that average. A smaller standard deviation means more consistent performance, regardless of whether they are distributing to More, Ratnadeep, or Q-Mart.
Solution
Imagine two cricket batsmen, Venkat and Lakshmi. Venkat (Team A) scores: 50, 52, 51, 49, 53, 50. His scores are all very close to each other. He's consistent. Lakshmi (Team B) scores: 30, 70, 40, 60, 20, 80. Her scores are all over the place – sometimes high, sometimes low. She's less consistent.
The mean is like their average score. The standard deviation tells us how "spread out" their scores are. A small spread means more consistency. We'll calculate these for Heritage Foods' sales teams.
Let's calculate the mean and standard deviation for both teams (sales in ₹1,00,000s).
Team A (Mr. Venkat Reddy: Hyderabad & Secunderabad): [50, 52, 51, 49, 53, 50]
- Mean (Average) for Team A: (50 + 52 + 51 + 49 + 53 + 50) / 6 = 305 / 6 = 50.83 (₹50,83,000)
- Standard Deviation for Team A:
- Differences from mean: (50-50.83), (52-50.83), (51-50.83), (49-50.83), (53-50.83), (50-50.83)
= -0.83, 1.17, 0.17, -1.83, 2.17, -0.83 - Squared differences: 0.69, 1.37, 0.03, 3.35, 4.71, 0.69
- Sum of squared differences: 0.69 + 1.37 + 0.03 + 3.35 + 4.71 + 0.69 = 10.84
- Variance (sum of squared differences / (n-1) for sample): 10.84 / 5 = 2.168
- Standard Deviation (sqrt(Variance)): √2.168 ≈ 1.47 (₹1,47,000)
- Differences from mean: (50-50.83), (52-50.83), (51-50.83), (49-50.83), (53-50.83), (50-50.83)
Team B (Ms. Lakshmi Prasad: Warangal, Karimnagar, Nizamabad): [30, 70, 40, 60, 20, 80]
- Mean (Average) for Team B: (30 + 70 + 40 + 60 + 20 + 80) / 6 = 300 / 6 = 50.00 (₹50,00,000)
- Standard Deviation for Team B:
- Differences from mean: (30-50), (70-50), (40-50), (60-50), (20-50), (80-50)
= -20, 20, -10, 10, -30, 30 - Squared differences: 400, 400, 100, 100, 900, 900
- Sum of squared differences: 400 + 400 + 100 + 100 + 900 + 900 = 2800
- Variance: 2800 / 5 = 560
- Standard Deviation: √560 ≈ 23.66 (₹23,66,000)
- Differences from mean: (30-50), (70-50), (40-50), (60-50), (20-50), (80-50)
Consistency:
Consistency is indicated by a lower standard deviation. A lower standard deviation means the sales figures are less spread out from the mean, indicating more predictable and stable performance.
- Team A Standard Deviation: ≈ 1.47
- Team B Standard Deviation: ≈ 23.66
Team A (Mr. Venkat Reddy's team) shows significantly more consistent performance in distributing dairy products like Heritage Ghee and Heritage Curd to supermarket chains (More, Ratnadeep, Q-Mart), as evidenced by its much smaller standard deviation.