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  1. ISEE Lower Level Quantitative Reasoning
  2. Interpret a table to identify a variable that can be averaged.

ISEE LOWER LEVEL • QUANTITATIVE REASONING

Interpret a table to identify a variable that can be averaged.

Learn to read a data table and figure out which column of numbers makes sense to average.

SECTION 1

Why Do We Organize Data in Tables?

People have been making lists and tables for thousands of years. Farmers in ancient times kept track of how many sheep they had. Merchants wrote down how much grain they sold each day.

Over time, people realized that organizing numbers in neat rows and columns made it much easier to spot patterns. A table is just a way to line up information so you can read it quickly.

3000 BC
Ancient Record Keeping
People in Mesopotamia used clay tablets to record counts of animals and crops in neat rows.
1600s
Scientists Use Tables
Scientists like Galileo started putting their experiment results into tables to find patterns.
1800s
Averages Become Popular
Mathematicians showed that finding the average of a group of numbers helps you understand the 'typical' value.
Today
Tables Are Everywhere
We see tables in school, in sports stats, on websites, and even on the ISEE test!

But here is the big question: when you look at a table full of data, which numbers actually make sense to average? Not every column of numbers should be averaged. Let's find out why!

SECTION 2

Core Ideas: Tables, Variables, and Averages

Before we dive in, let's learn three important words you will see on the ISEE.

1

Table

A table organizes information into rows (going across) and columns (going down). Each column has a header that tells you what kind of data is in it.
2

Variable

A variable is something that can change or be different from one item to the next. In a table, each column usually shows a different variable, like name, age, or score.
3

Average (Mean)

The average is a single number that represents the 'middle' or 'typical' value. You find it by adding up all the numbers and dividing by how many numbers there are.
4

Which Variables Can Be Averaged?

Only number variables that measure something can be averaged. You cannot average names, colors, or jersey numbers because adding them together doesn't make sense.
✦ KEY TAKEAWAY
Think of it like a fruit bowl. You can find the average weight of the fruits because weight is a measurement. But you can't average the names of the fruits — what would the 'average' of apple, banana, and grape even mean? If adding the numbers together makes sense, you can average them!
SECTION 3

See It: A Table with Different Kinds of Variables

Let's look at a table about students in a classroom. Some columns have numbers you can average. Other columns do not. Can you spot the difference?

Students in Ms. Garcia's ClassNameFav. ColorTest ScoreBooks ReadMiaBlue885LiamRed927ZoeGreen753NoahBlue856✗ Can't average✗ Can't average✓ CAN average!✓ CAN average!Names and colors are categories — they are NOT measurements.Test scores and books read are measurements — they CAN be averaged.
The green boxes mark columns that can be averaged (Test Score and Books Read). The red dashed boxes mark columns that cannot be averaged (Name and Favorite Color).

Notice that Test Score and Books Read are both numbers that measure something. Adding 88 + 92 + 75 + 85 makes sense! But adding "Mia + Liam + Zoe + Noah" does not make sense at all.

SECTION 4

How to Find the Average

Once you know which variable can be averaged, here is the formula. It's simple!

AVERAGE FORMULA
Average = Sum of all values ÷ Number of values
Sum means the total when you add up all the numbers. Number of values means how many numbers you added together.

Let's try it with the Test Scores from our table: 88, 92, 75, and 85.

STEP 1 — ADD
88 + 92 + 75 + 85 = 340
We added the four test scores together to get a sum of 340.
STEP 2 — DIVIDE
340 ÷ 4 = 85
We divided by 4 because there are 4 students. The average test score is 85.
💡 ISEE Test Tip
On the ISEE, you might not even need to calculate the average. The question might just ask which column can be averaged. Look for columns with numbers that measure or count something. Skip columns with names, labels, or categories!
SECTION 5

Sorting Variables: Can You Average It?

Not all numbers can be averaged! Some numbers are just labels, like jersey numbers or phone numbers. Let's see a handy chart that shows the difference.

Can You Average This Variable?Ask yourself: Does adding these numbers together make sense?✓ YES — Can Average✗ NO — Cannot AverageTest Scores85, 92, 78 → measures knowledgeStudent NamesMia, Liam, Zoe → words, not numbersHeights (inches)48, 52, 50 → measures how tallFavorite ColorsRed, Blue, Green → categoriesMinutes of Practice30, 45, 20 → measures time spentJersey Numbers7, 23, 11 → labels, not measurementsPrices ($)$3, $5, $2 → measures costPhone Numbers555-1234 → digits, not amounts🔑 Quick RuleIf the numbers MEASURE or COUNT something, you CAN average them!
Green boxes show variables that measure or count — these can be averaged. Red boxes show labels or categories — these cannot be averaged.

Here's a trick: jersey numbers look like regular numbers, but they're really just labels. The average of jersey numbers 7, 23, and 11 doesn't tell you anything useful. Always ask: does this number measure or count something?

SECTION 6

Worked Example: Finding the Right Variable

Let's walk through a problem just like one you might see on the ISEE. Follow along step by step!

Animals at the Pet Shelter
AnimalTypeWeight (lbs)Cage Number
BuddyDog403
WhiskersCat107
RexDog551
DaisyRabbit512

Question: Which variable in this table can be averaged to find a meaningful result?

Solving the Problem

Step 1 — Read the column headers

The four columns are: Animal (name), Type (kind of animal), Weight in pounds, and Cage Number. Read each header carefully.

Step 2 — Check each variable

Animal: These are names (Buddy, Whiskers, Rex, Daisy). You can't add names. ✗ Type: These are categories (Dog, Cat, Rabbit). You can't add categories. ✗ Weight: These are measurements in pounds (40, 10, 55, 5). Adding them makes sense! ✓ Cage Number: These are labels for cages, not measurements. The 'average cage number' doesn't mean anything useful. ✗

Step 3 — Pick the answer

The only variable that measures something is Weight (lbs). That is the variable that can be averaged.
Answer: Weight (lbs) — the average weight would be (40 + 10 + 55 + 5) ÷ 4 = 110 ÷ 4 = 27.5 lbs.
SECTION 7

Tips, Traps, and Test Strategies

The ISEE sometimes tries to trick you. Here are common traps and how to avoid them.

TrapWhy It's TrickyHow to Avoid It
Numbers that are labelsJersey numbers, room numbers, and zip codes look like regular numbers.Ask: does this number measure or count anything? If not, skip it.
Two columns that can be averagedA table might have more than one column you could average.Read the question carefully. It may ask about a specific variable.
Picking the biggest numbersSome kids pick the column with the largest numbers.Size doesn't matter — what matters is whether the numbers measure something.
🎯 ISEE STRATEGY
Use process of elimination! Cross out any answer choice that is a name, a category, or a label number. Whatever is left should be a measurement or a count — that's your answer. Remember, on the ISEE there is no penalty for guessing, so always pick an answer even if you aren't sure!
SECTION 8

Beyond Averages: Other Things You Can Do with Data

Finding the average is just one way to understand data. As you keep learning math, you will discover other tools too. Here's a sneak peek!

What You Know NowWhat You'll Learn Later
Average (Mean) — add up and divideMedian — the middle number when sorted
Reading a table to find one variableComparing two variables in a scatter plot
Identifying which variable to averageDeciding which graph type fits the data best

For the ISEE Lower Level, you mostly need to know the average (mean). But learning to spot which variable to work with is a skill that will help you in every math class going forward. Great job learning this!

SECTION 9

Practice Problems

Time to test yourself! Read each question carefully. Remember: look for numbers that measure or count something.

PROBLEM 1 — CONCEPTUAL
A table shows the following columns about students: Name, Age, Favorite Sport, and Shoe Size. Which variable can be averaged?
PROBLEM 2 — BASIC CALCULATION
A table lists four dogs: Spot (weight 25 lbs), Max (weight 40 lbs), Bella (weight 30 lbs), and Duke (weight 45 lbs). What is the average weight of the dogs?
PROBLEM 3 — INTERMEDIATE
A table about a soccer team has these columns: Player Name, Jersey Number, Goals Scored, and Position. Which column could you average to find something meaningful about the team?
PROBLEM 4 — APPLIED
Sara's class made a table about their favorite books. The columns are: Book Title, Number of Pages, Genre, and Student Rating (out of 5 stars). Sara wants to know the typical rating. Which variable should she average?
PROBLEM 5 — CRITICAL THINKING
A table about a bake sale has these columns: Baker's Name, Item Sold, Number Sold, Price per Item, and Table Number. Tom says, 'We can average the Table Number to see which table did best.' Is Tom correct?
SUMMARY

Lesson Summary

A table organizes data into rows and columns. Each column is a variable — something that can change from row to row. To find the average, add up all the values and divide by how many there are. But only variables that measure or count something can be averaged. Names, categories, and label numbers (like jersey numbers) cannot be averaged.

On the ISEE, always ask yourself: Does adding these numbers together make sense? Use process of elimination to cross out answer choices that are words or labels. Pick the column with real measurements or counts. You've got this!

Varsity Tutors • ISEE Lower Level • Interpret a table to identify a variable that can be averaged.