Q.Find the mean, median and mode of the following data on the number of complaints received per day at a customer-service desk over 9 days: 3, 5, 7, 5, 9, 5, 6, 8, 4.

Compute the mean by summing and dividing by $n$, find the median by arranging in order, and find the mode as the most frequent value.

Mean $=52/9\approx5.78$. Ordered data: 3,4,5,5,5,6,7,8,9 — median (5th value) $=5$. Mode $=5$ (appears 3 times).

Step 1 — Find the mean. Sum $=3+5+7+5+9+5+6+8+4 = 52$. $n=9$. $\bar x = 52/9 \approx 5.78$.

Step 2 — Find the median. Arrange the data in ascending order: $3,4,5,5,5,6,7,8,9$. With $n=9$ (odd), the median is the $\left(\dfrac{9+1}{2}\right)^{\text{th}} = 5^{\text{th}}$ value in this ordered list, which is $5$.

Step 3 — Find the mode. Counting frequencies: $3$ (once), $4$ (once), $5$ (three times), $6$ (once), $7$ (once), $8$ (once), $9$ (once). The value $5$ occurs most often (3 times), so Mode $=5$.

Independent check (empirical relationship). $3\,\text{Median}-2\,\text{Mean} = 3(5)-2(5.78) = 15-11.56=3.44$, which is reasonably close to the actual mode of $5$ — the empirical relation is only approximate for real data and mainly intended for moderately skewed distributions, so a rough (not exact) match here is expected and not a sign of an arithmetic error, given this small, only mildly skewed data set.

Forgetting to sort the data before picking the middle value for the median (using the original, unsorted order instead) gives a completely wrong median — sorting is always the first, non-negotiable step of a median calculation.