1.) The mode is the number that's most frequent in a given list. In our list, we have 2, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9, 10. Our most frequent number is 6; therefore, our mode is 6.
2.) The median is the number in the middle of a list organized from least to greatest. 2, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9, 10; 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 9; 4, 5, 5, 5, 6, 6, 6, 6, 7; 5, 5, 5, 6, 6, 6, 6; 5, 5, 6, 6, 6; 5, 6, 6; 6. 6 is our median.
I hope this helps, despite your answer choices not providing the correct answer.
From the diagram, we shall determine the value of 'x'. This can be obtained by using the pythagoras theory as follow:
x² = 5² + 12²
x² = 25 + 144
x² = 169
Take the square root of both side
x = √169
x = 13 m
Finally, we shall determine the original height of the tree. This can be obtained as follow.
From the question given above, the tree was broken from a height of 5 m from the ground which form a right angle triangle with x being the Hypothenus as illustrated in the diagram.
Thus, the original height of the will be the sum of 5 and x i.e
Height = 5 + x
x = 13 m
Height = 5 + 13
Height = 18 m
Therefore, the original height of the tree is 18 m.