Using estimators for goodness of fit test

[Clarkson]

This is a practice question I came across when dong some goodness of fit test examples.A company sells cloths by mail order.The size of clothes is defined by hip size; thus the height of customers of a particular customer may vary considerably.
Data set of heights sent in by customers of size 18 is given.Data set includes class interval,class mid mark and frequency.

The company decides that it is not possible to produce a range of garments for a particular size suitable for customers of different heights.A single height must be chosen and it is proposed that mean height should be chosen for this.Comment on this suggestion as it applies to customers of size 18 and make an alternative proposal.


Please help me to answer this part.I was able to answer other parts in this question but I don't know what else can be used other than the mean height

 

[Karabiner]

I suppose it depends on the actual intervals and the frequencies. The
size should maybe be chosen in a way to minimize the number of customers
very far from it. If the distribution is heavily skewed, then the mean is dragged
away from where most of the customers are found. For a start, you could make
a bar graph with intervals at the x-axis and frequencies at the y-axis. If this
appears skewed, then you could look at the frequencies for the interval which
contains the mean and for its 2 neighbouring intervals, and then do the same for
the interval which contains the median and at its 2 neighbouring intervals.
Or some other value than the median may be appropriate.

With kind regards

K.