# A guide to essential statistics for counsellors

The university application process is filled with data. In order to provide informed guidance, counsellors need a basic understanding of statistics

#### Yein Oh

The university application process is filled with data. To understand this data well, and use it to provide informed guidance, a basic understanding of statistics is essential for counsellors.

We probably learned how to use statistics back in our own high-school mathematics classes. But revisiting these concepts and understanding how they apply in the university counselling context can be useful.

This article will touch upon key statistical concepts that surface often in university counselling, with advice on how to approach them more thoughtfully.

### Acceptance rate

The first statistic most counsellors are likely to think of is **acceptance rate. **The definition is deceptively simple: the number of accepted students divided by the number of total applicants.

Students and parents use this number, often derived from a quick Google search, as a benchmark to assess how competitive a university is and subsequently to make their own university lists. Other than the glaring fact that a Google search might yield unofficial and therefore incorrect results, this can be a misleading move as they are not considering **samples** and **population**.

The number of total applicants in the acceptance rate calculation is a compilation of many samples, each representing a different group of students. Acceptance rates can change according to which group your student falls into (domestic vs international, for example).

Unfortunately, this might yield a lower acceptance rate for your students than they expect, so advise them against using easily available acceptance rates as benchmarks for their application planning.

### Mean and median

Other key statistical terms are **mean **and** median, **which are part of measures of central tendency – basically, numbers that are a centre point, or a typical value in a dataset.

We’re probably most familiar with the **arithmetic mean**, or **average**, gained by adding up all the numbers and dividing that by the number of objects in the collection. We see means everywhere, from mean GPA in an incoming class profile (class profile for University of San Francisco) to the average financial aid for non-citizens.

We derive a **median** when we order the data from the smallest to largest and find the data point that has an equal number of values above and below it.

Why would we use median instead of a mean? Medians are much less affected by **outliers, **data points that are extremely high or low. When outliers are present in a dataset (this means that the dataset is probably not symmetrical and is therefore **skewed**), the value of the mean will be sharply pulled to the direction where outliers are present, but the value of a median will stay as it is.

You can see how UCLA reports the median – not mean – GPA for it incoming class profile, and MIT reports its median scholarship amount. There were probably some outliers in this data.

For test scores, reporting the **middle 50 per cent range** is even more common. The middle 50 per cent is a range of values, from the 25th percentile to the 75th (more on percentiles later). This range is also less affected by outliers and provides more information than a single data point, such as a mean or median. So it makes sense that this might be an even more popular statistic than mean or median. For example, Purdue chose to do this with its GPA and test scores, and College Board’s Big Future tool reports the middle 50 per cent range of test scores to paint a descriptive picture of the successful applicant at a university.

Using mean, median and middle 50 percentile GPA can be helpful in guiding your students’ application journeys in a couple ways. The key is to first research the average GPA and test score of an incoming class at their target university, then compare that with your student’s profile. Presenting the data in such a way can help manage expectations when students are aiming for very selective universities without a clear idea of the difficulty of being accepted.

This can also facilitate the strategic building of a university list based on “reach”, “target” and “safety” categories.

Additionally, when you’re working with students who need financial aid to attend university, the average value of financial aid awarded will also be useful data to consider when further building a university list. However, do keep in mind that, while the average is a typical value, your student might not necessarily end up getting that exact amount with their offer letter.

### Distributions

**Frequency distributions** are displays of the number of observations or individuals in each category in a table or a graph format. Examples include the IB statistical bulletin and AP Scores Distributions.

You can use this to help your students put their scores in context. As these distributions can go into great detail (especially the IB statistical bulletin), you can also use it to gain a deeper understanding of the system at hand, as well as the difficulty of an individual test on a more granular level (for example, to look at the percentage of students who got the highest score possible for a certain subject).

Note that frequency distributions are conceptually different from **probability distributions, **a prime example of which is the normal distribution. This is beyond the scope of this article, but just keep in mind that not all distributions are the same.

### Percentiles

**Percentiles** were mentioned earlier when explaining the middle 50 per cent. Percentiles are simply the number where a certain percentage of scores falls below that number. Selective universities like to report that their average incoming class was drawn from the upper percentile.

For instance, 95 per cent of Yale’s incoming class comes from the top 10 per cent of its graduating class, and 92 per cent of UNC Chapel Hill’s incoming class comes from the top 20 per cent.

Percentiles can be especially useful to work with as a counsellor. For instance, when discussing with a student whether or not to submit a test score with an application, you can point to what percentile the test score corresponds to and see whether that percentile is higher or lower than their existing GPA or IB score. If it is lower, then the test score won’t necessarily be a good supplement, but if the percentile is higher, then it can be a useful additional demonstration of the student’s cognitive abilities.

Painting a picture of the student’s academic abilities with percentiles in recommendation letters can also be helpful for admissions officers to better understand the student, especially if your school does not calculate rank – but only if doing so helps the student (for example, “Maria is clearly a student in the top 10 per cent of the class”).

Finally, I tell students to report any percentiles, if possible, of their own achievements to put them in context (for example, “I scored in the top 15 per cent of the applicants in the final round of the competition”). It’s part of quantifying your success and helps to tell a convincing story and create a more successful application.