Statistics I

6 appears three times, 4 appears twice, and 7 and 9 appear once each. The most frequent value is 6.

In order the data is $3, 7, 9, 11, 15$. With five values the middle one is the third, which is 9.

The total is $14 + 18 + 11 + 17 = 60$, and there are 4 values, so the mean is $60 \div 4 = 15$.

Largest is 8, smallest is $-6$. Range $= 8 - (-6) = 8 + 6 = 14$. Subtracting a negative adds.

$\sum fx = 8 + 18 + 20 + 25 = 71$ and $\sum f = 20$, so the mean is $71 \div 20 = 3.55$.

The six numbers total $6 \times 9 = 54$. The seven numbers total $7 \times 10 = 70$. The added number is $70 - 54 = 16$.