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A point estimate is :

A single numerical value that is used to estimate the corresponding population parameter.

Whereas an interval estimate is :

An estimate that consists of two numerical values defining a range of values that, with a specified degree of confidence, most likely include the parameter being estimated.

My question is what makes interval estimates more meaningful for estimation than point estimates?

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    $\begingroup$ Your question does not compute. A point estimate represents something different than an interval, these are not comparable. What is "better" depends on what your goal is. $\endgroup$ Oct 23, 2020 at 9:52
  • $\begingroup$ My book mentions that it is more meaningul to estimate the population mean using an interval than just a point estimate of the sample mean @user2974951 . $\endgroup$
    – Positron12
    Oct 23, 2020 at 9:54
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    $\begingroup$ "Meaningful" is different from "better". Even so, that is debatable, if you are interested in the point estimate than this is the best tool for the job. But I understand what the author wanted to say, an interval captures more information than a point, so it could be more meaningful, especially if the process is very variable. $\endgroup$ Oct 23, 2020 at 9:57
  • $\begingroup$ I edited the question. @user2974951 $\endgroup$
    – Positron12
    Oct 23, 2020 at 9:59

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Often the point estimate is the primary goal and the interval (or error estimate) is auxilliary meta-information which tells us something about the point estimate (the accuracy/uncertainty).

For instance:

  • An ice-cream producer needs to place an order for some amount of sugar. He can decide on the quantity by using some estimates for the number of ice-creams that he will be selling, which relates to the amount of ingredients he needs.

    Will this ice-cream producer place his order using an interval "I would like to buy between 1200 and 1250 kg sugar, please" or will the ice-cream producer use some fixed number "I would like to buy 1225 kg sugar, please"?


What's the advantage of a point estimate over an interval estimate?

Point estimates and interval estimates are not really be substitutes for eachother. They are not compared in a sense like advantages and disadvantages for a particular problem and based on that the one estimate is selected instead of the other. The point estimate and interval estimates serve different purposes.

My question is what makes interval estimates more meaningful for estimation than point estimates?

You could view an interval estimate as providing extra information about the estimate. It is not only pointing out the region/point where the parameter is most likely estimated, it also provides information about the accuracy of this estimate. In that sense it contains more information and is more meaningfull.

An interesting argument has been made by Neyman (in "Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability") while formulating confidence intervals he wrote something that estimation is not just about point estimates, but instead about ranges.

This shows that what the statisticians have really in mind in problems of estimation is not the idea of a unique estimate but that of two estimates of the form, say $$\underline\theta = T - k_1S_t \quad \text{and} \quad \overline\theta = T + k_2S_t $$

Often we do not just want to know a point estimate, but we also want to know the error of that point. So this error or a range is also the information from the data that we want to convey/compute and is what makes a point estimate meaningful (without knowing anything about accuracy a single point is not very useful).

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