Finding the specific height of a subject using the mean and total number of subjects

Hi everyone,

I think this will be a very basic question for most of you, but I am not the best at maths. I shall provide the question and my attempt at a solution:

Question: "The mean height of 9 female subjects in a room is 167.33 cm. One subject leaves the room. The mean height is now 167.75 cm. What is the height of the female who left the room?"

My attempt:

I figure we could find the change in x (number of subjects) over the change in y (the mean) and then use the answer and subtract it from the original mean:

So: change in x = 9 - 8 = 1

Change in y = 167.75 - 167.33 = 0.42

Thus: 1 / 0.42

Therefore, to find the height of the subject that left we could simply perform the operation: 167.33 - (1/0.42) = 164.5

However, when I submit that answer into the online quiz I am doing, it says the answer is incorrect.

Any help on this issue will be much appreciated! Is my method incorrect?

Thanks,

Ben

Re: Finding the specific height of a subject using the mean and total number of subje

When there are 9 people in the room, the mean height is 167.33cm. This means that the total height of all 9 people is 9 x 167.33cm = 1505.97cm

Then when one of the people leaves, there are 8 remaining in the room. The new mean height is 167.75cm. This means that the total height of all remaining 8 people is 8 x 167.75cm = 1342cm.

So the total height decreased from 1505.97cm to 1342cm when the person left the room. So she must have been 1342cm - 1505.97cm = 163.97cm tall.