A tech startup’s daily active users (DAU) over a week were: 12,500, 14,200, 13,800, 15,100, 16,400, 15,900, 17,300. What is the mean absolute deviation (MAD) of DAU from the mean? - AIKO, infinite ways to autonomy.

Understanding the Context

Here’s a summary of the DAU data for easy review:

| Day | DAU |
|-----|---------|
| 1 | 12,500 |
| 2 | 14,200 |
| 3 | 13,800 |
| 4 | 15,100 |
| 5 | 16,400 |
| 6 | 15,900 |
| 7 | 17,300 |

Total DAU over the week:
12,500 + 14,200 + 13,800 + 15,100 + 16,400 + 15,900 + 17,300 = 105,000

Calculating the Mean (Average DAU)

Key Insights

Mean = Total DAU / Number of Days
Mean = 105,000 / 7 = 15,000

The average daily active user count is 15,000 — a strong baseline indicating consistent user engagement.

Mean Absolute Deviation (MAD) – A Measure of Variability

MAD quantifies how much DAU deviates from the mean, offering insight into user activity volatility. It is calculated as follows:

1. Compute absolute deviations of each day’s DAU from the mean (15,000):
   | Day | DAU | |DAU – Mean| |
   |-----|--------|-----------|------------|
   | 1 | 12,500 | |12,500 – 15,000| = 2,500 |
   | 2 | 14,200 | |14,200 – 15,000| = 800 |
   | 3 | 13,800 | |13,800 – 15,000| = 1,200 |
   | 4 | 15,100 | |15,100 – 15,000| = 100 |
   | 5 | 16,400 | |16,400 – 15,000| = 1,400 |
   | 6 | 15,900 | |15,900 – 15,000| = 900 |
   | 7 | 17,300 | |17,300 – 15,000| = 2,300 |

Final Thoughts

2. Sum of absolute deviations:
   2,500 + 800 + 1,200 + 100 + 1,400 + 900 + 2,300 = 8,100

3. MAD = Total absolute deviations / Number of days
   MAD = 8,100 / 7 = 1,157.14

Interpretation

With a Mean Absolute Deviation of approximately 1,157, the DAU exhibits low to moderate variability around the weekly average. This means user counts tend to hover closely near 15,000, suggesting strong and stable daily engagement—ideal for a growing startup. Such consistency strengthens confidence in user retention and product-market fit, and helps inform predictable planning for marketing and development efforts.

Conclusion:
Tracking DAU is essential for tech startups, and combining raw numbers with statistical measures like MAD provides a clearer, data-driven picture. For this startup, daily active users remained remarkably consistent over the week, with an average of 15,000 and minimal swing—marking a solid foundation for sustained growth and scalability.