Answer
$\underline{\text{Mean}}:6$
$\underline{\text{Median}}: 7$
$\underline{\text{Mode}}: \text{None}$
Work Step by Step
$\underline{\text{Mean}}:$
$\text{Mean}$ = $\dfrac{\text{Sum of all observations}}{\text{Total no. of observations}}$ = $\dfrac{1+2+5+7+8+9+10}{7}=\dfrac{42}{7}=\boxed{6}$
$\underline{\text{Median}}:$
$\text{We can find the median by first arranging the given observation in the increasing order and find the mid-point of these observations. In this case, we get it as}$
$1, 2, 5, 7, 8, 9, 10$
$\text{There are 7 observations. So, the mid-point of these observations is given as}$
$\text{Mid-point} =\dfrac{n+1}{2}=\dfrac{7+1}{2}=\dfrac{8}{2}=4$.
$\text{We have found out that the $3^{\text{rd}}$ observation of the arranged number is the median. The $3^{\text{rd}}$ observation in this arranged numbers is 18. That means, the median of this problem is $\boxed{7}$}$.
$\underline{\text{Mode}}:$
$\text{Mode is the number that occurs the most. In this case, there is no number that occurs more than once. So, the mode of this question is $\boxed{\text{none}}$}$
