Practice30 Create account

The mean of the squares of the first n natural numbers is 63. What is n?

Competition practiceStatistics

A13
B12
C14
D9

Step-by-Step Solution

Mean of

1^{2}, \dots, n^{2}

is

\frac{( n + 1 ) ( 2 n + 1 )}{6}

. Setting it to 63:

(n + 1) (2 n + 1) = 378. n = 13

gives

14 \times 27 = 378

. ✓

Answer: A) 13

Master this topic in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Statistics practice questions

More Statistics practice

Two numbers have an arithmetic mean of 25 and a geometric mean of 15. What is the larger…Shreya logged her weekly running distance for 10 weeks; the mean was 18 km. When she…Five positive integers have a mean of 18 and a median of 20, and 22 is their only mode.…Five positive integers have a mean of 10 and a median of 12, and their only mode is 15.…For the values x = 5, 10, 15, 20, 25 with frequencies 4, 9, f, 5, 3, the median is 15.…