What is the approx average of different probable heights of Gopi?

[Ganesh Ujwal]

In Gopi's opinion his height is greater than 168 cm but less than 178 cm. His siter does not agree with Gopi and she thinks that Gopi's height is greater than 172 cm but less than 176 cm. His mother's view is that his height cannot be greater than 175 cm. If all of them are correct in their estimation, and Gopi's height is an integer value. What is the approx average of different probable heights of Gopi? [Ans: 174 cm]

My Try: Average of Gopi's opinion: \(\displaystyle \frac {168 + 178}{2}\)

Average of Gopi's sister's opinion: \(\displaystyle \frac {172 + 176}{2}\)

Average of Gopi's mother opinion: \(\displaystyle \frac {175}{1} = 175\)
The approx average of different probable heights of Gopi = \(\displaystyle \Large\frac {\frac {168 + 178}{2} + \frac {172 + 176}{2} + \frac {175}{1}} {3}\)

Is my procedure is right? If not, tell the correct procedure.

 

[Dr.Peterson]

In Gopi's opinion his height is greater than 168 cm but less than 178 cm. His siter does not agree with Gopi and she thinks that Gopi's height is greater than 172 cm but less than 176 cm. His mother's view is that his height cannot be greater than 175 cm. If all of them are correct in their estimation, and Gopi's height is an integer value. What is the approx average of different probable heights of Gopi? [Ans: 174 cm]

My Try: Average of Gopi's opinion: \(\displaystyle \frac {168 + 178}{2}\)

Average of Gopi's sister's opinion: \(\displaystyle \frac {172 + 176}{2}\)

Average of Gopi's mother opinion: \(\displaystyle \frac {175}{1} = 175\)
The approx average of different probable heights of Gopi = \(\displaystyle \Large\frac {\frac {168 + 178}{2} + \frac {172 + 176}{2} + \frac {175}{1}} {3}\)

Is my procedure is right? If not, tell the correct procedure.

First list the different possible (I think that's really what they mean, not probable) integer values -- that is, the integers that satisfy all of the intervals, since we are assuming they are all correct. Then average just those integers. You will get 174.

They aren't telling you to average averages. The word "probable" is confusing.

 

[JeffM]

In Gopi's opinion his height is greater than 168 cm but less than 178 cm. His siter does not agree with Gopi and she thinks that Gopi's height is greater than 172 cm but less than 176 cm. His mother's view is that his height cannot be greater than 175 cm. If all of them are correct in their estimation, and Gopi's height is an integer value. What is the approx average of different probable heights of Gopi? [Ans: 174 cm]

My Try: Average of Gopi's opinion: \(\displaystyle \frac {168 + 178}{2}\)

Average of Gopi's sister's opinion: \(\displaystyle \frac {172 + 176}{2}\)

Average of Gopi's mother opinion: \(\displaystyle \frac {175}{1} = 175\)
The approx average of different probable heights of Gopi = \(\displaystyle \Large\frac {\frac {168 + 178}{2} + \frac {172 + 176}{2} + \frac {175}{1}} {3}\)

Is my procedure is right? If not, tell the correct procedure.

The question makes no sense. For example, what is the definition of an "approximate average" and how does it differ from an arithmetic mean or a weighted average? The second to last sentence has a subordinate clause but no main clause and so is not even grammatically meaningful in English. Does "probable" really mean "possible"?

Your answer certainly makes no sense. For example, if Gopi estimates that his height is greater than 168 cm and less than 178 cm, his estimate is correct, and his actual height is an integer number of centimeters, then his height is neither 168 cm nor 178 cm. Consequently, what is the logic of including those two numbers in your computation?

If a question along the lines of "if each estimate is correct and Gopi's height is an integer number of centimeters, what is the arithmetic mean of his possible heights" is what was intended, then the first thing to do is to determine what those possible heights are. What is your answer to that preliminary question if you would be so kind?