Q.The marks obtained (out of 100) by 7 students in a class test are: 45, 52, 38, 60, 41, 55, 49. Find the arithmetic mean of the marks.

This is a set of 7 individual observations, so the mean is simply the total of all the marks divided by the number of students.

$45+52+38+60+41+55+49 = 340$

$\bar{x} = \dfrac{340}{7} \approx 48.57$

We are given $n = 7$ individual observations (not a frequency distribution), so the arithmetic mean formula to use is $\bar{x} = \dfrac{\sum x}{n}$.

Step 1 — Add the observations.

Adding in pairs: $45+52=97$, $97+38=135$, $135+60=195$, $195+41=236$, $236+55=291$, $291+49=340$.

So $\sum x = 340$.

Step 2 — Divide by the number of observations.

Independent check. Re-adding the same 7 numbers in a different grouping: $(38+41)+(45+49)+(52+55)+60 = 79+94+107+60 = 340$ — the same total, confirming the sum, and hence the mean, is correct.

Dividing by the wrong count (e.g. using 6 instead of 7 students) is the most common slip — always count the observations before dividing. Also avoid rounding intermediate sums; keep the exact total (340) and only round the final quotient.