A statistics question, expectation/average vs. mode

[Agent Smith]

Ben keeps track of the number of customers who visit his shop on a given day:

Number of customers	Number of days
0	10
2	10
3	20

The average number of customers/day who visit Ben's shop = [imath]\frac{0 \times 10 + 2 \times 10 + 3 \times 20}{10 + 10 + 20} = 2[/imath]

The mode number of customers is [imath]3[/imath] (most common number in our data).

The explanation in the book says that in the long term Ben sees around 2 customers (average/mean/expectation), but on any given day he should see around 3 customers (mode). How might these different pieces of information be useful for Ben in running his shop?

 

[lev888]

Ben keeps track of the number of customers who visit his shop on a given day:

Number of customers	Number of days
0	10
2	10
3	20

The average number of customers/day who visit Ben's shop = [imath]\frac{0 \times 10 + 2 \times 10 + 3 \times 20}{10 + 10 + 20} = 2[/imath]

The mode number of customers is [imath]3[/imath] (most common number in our data).

The explanation in the book says that in the long term Ben sees around 2 customers (average/mean/expectation), but on any given day he should see around 3 customers (mode). How might these different pieces of information be useful for Ben in running his shop?

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[Agent Smith]

It's not a homework problem. It's a doubt that I need help on. They're both (mode & mean) measures of central tendency but they have different values and so cogito recommend different strategies for Ben. Where should Ben use the mean and where should Ben use the mode?

 

[lev888]

Ben keeps track of the number of customers who visit his shop on a given day:

Number of customers	Number of days
0	10
2	10
3	20

The average number of customers/day who visit Ben's shop = [imath]\frac{0 \times 10 + 2 \times 10 + 3 \times 20}{10 + 10 + 20} = 2[/imath]

The mode number of customers is [imath]3[/imath] (most common number in our data).

The explanation in the book says that in the long term Ben sees around 2 customers (average/mean/expectation), but on any given day he should see around 3 customers (mode). How might these different pieces of information be useful for Ben in running his shop?

Average of around 2 per day - ok. He can use it to make all sorts of business decisions (hiring help, ordering supplies, etc).
Mode - I wouldn't describe it as "around 3 on any given day". First, it's exactly 3, since mode is one of the values. Second, what if the number of days for 3 customers was 11 and not 20? It would still be the mode, but he would have almost the same chances of seeing 0, 2 or 3 customers on any given day. Can't think of a use case for mode.

 

[khansaheb]

Statistical analysis cannot produce any "significant" answer with such limited observation.

 

[Agent Smith]

Can't think of a use case for mode.

@khansaheb

Statistical analysis cannot produce any "significant" answer with such limited observation.

These are simplifications the question makes.

The mean takes into account all of the data and from the calculations I did on the side provides an accurate account of (say) income. The mode focuses only on the most common data points (there are 20 of 3 customers).