TEAS Measurement and Data study guide

What this topic actually asks of you

Measurement and data is one of the two sub-content areas of the ATI TEAS Mathematics section. ATI publishes its size: it is 11% of the exam and 16 of the 34 scored math questions. The whole Math section is 38 items (34 scored, 4 unscored) and is timed separately — 57 minutes.

Two things follow, and they shape how to study it.

• The arithmetic is small; the unit is the question. Almost every item here is a conversion, a rate, or a formula. The numbers are easy; the points are lost in the unit factor — multiplying where you divide, using pounds as kilograms, or reading the wrong row on a table.
• ATI publishes only a sample of the formulas. ATI lists a partial set "from the ATI TEAS® Study Manual": distance (d = rt), the area of a rectangle and of a triangle, the perimeter of a square, the volume of a rectangular prism, and the circumference of a circle. This topic teaches those, plus the unit conversions they are used with.

Our practice items are single-answer. The real ATI TEAS also uses other item types: ATI's own content outline lists multiple-choice, multiple-select, fill-in-the-blank numeric, hot spot and ordered-response items. Elk Ridge Academy's practice items are single-answer only, and they are text-only — a data question states its table as text, with no picture or graph — so treat the method, not any one format, as the thing you are drilling.

The twelve procedures

Every practice item in this topic is one of these twelve. Each is worked out in full below — the rule, the steps, and the trap it sets.

1. Metric conversions — mg, mcg, g, kg, mL and L. One gram is 1,000 milligrams, and one liter is 1,000 milliliters; convert the unit before you compute. → example 1
2. Household and mass conversions — pounds to kilograms (≈ 2.2 lb per kg), teaspoons and tablespoons (1 tbsp = 3 tsp), and fluid ounces and cups (1 cup = 8 fl oz, 1 fl oz ≈ 30 mL). → example 2
3. Temperature conversions — between Celsius and Fahrenheit, both directions. → example 3
4. Rate and time — d = rt: rearrange it to find distance, speed, or time; match the time unit to the rate. → example 4
5. Area and perimeter — area of a rectangle (A = lw) and a triangle (A = ½bh) in square units; perimeter of a square (P = 4s) in linear units. → example 5
6. Volume — the volume of a rectangular prism (V = lwh) in cubic units. → example 6
7. Circumference of a circle — C = 2πr, with π ≈ 3.14 unless the question says otherwise. → example 7
8. Reading data — find the row or column the question names, then read the value or total. → example 8
9. Mean, median and mode — the average (total ÷ count), the middle value (sort first), and the most common value. → example 9
10. Range — the spread of a data set: the largest value minus the smallest. → example 10
11. The relationship between two variables — whether two quantities rise together (a positive relationship), move oppositely (a negative relationship), or stay flat (constant), and how to read a rate of change from a table. → example 11
12. The area of a circle — A = πr², in square units; the companion to the circumference. → example 12

The conversions to know

Clinical practice rounds the household factors; the metric factors are exact. The rounded figures below are the clinical convention the practice items use, not the exact SI value (NIST SP 811 gives 1 lb = 0.45359237 kg and 1 fl oz = 29.5735 mL), which is why they carry "≈".

Source: NIST SP 811, Guide for the Use of the International System of Units (SI) — the metric factors are its exact values; the household factors (2.2 lb, 0.45 kg, 15 mL and 30 mL) are the rounded clinical convention this course uses, not SP 811 values. The 2.2 lb / 0.45 kg pair is rounded on each side, so the two are close to, but not exactly, each other's reciprocal. Accessed 2026-10-07.

A four-step method

1. Find the question mark. Name the one quantity being asked for, and its unit. "The dose, in milliliters." "The mean, in steps."

This step defeats the classic wrong answer on this topic: the right arithmetic on the wrong quantity — the perimeter instead of the area, the median instead of the mean, a temperature when a change in temperature was asked for.

2. Write down what you are given, each with its unit. Conversions and rates are where a missing unit hides: 2.5 g and 2.5 mg are a thousand apart, and a rate of "per hour" with a time in minutes is a factor of 60 wrong.

3. Convert first, then compute. In a conversion or a rate, change every quantity to the unit the answer needs before you multiply or divide. Do not mix units of the same kind in one formula.

4. Check the answer for size and unit. Is a one-gram dose written in milligrams a big number? Is a perimeter in square units? Put the answer back into the story and ask whether it is the right size and the right kind of unit.

The twelve worked examples

1. Metric conversions — move the decimal the right number of places

Convert 2.5 g to milligrams.

• One gram is 1,000 milligrams, so multiply: 2.5 × 1,000.
• 2.5 × 1,000 = 2,500 mg.
• Check the direction: a milligram is smaller than a gram, so the number gets bigger. 2,500 is bigger than 2.5 ✓.

The trap: dividing instead of multiplying (2.5 ÷ 1,000 = 0.0025 mg). Going to a smaller unit gives a larger number.

2. Household and mass conversions — pounds to kilograms, spoons to spoons

A patient weighs 154 lb. What is the weight in kilograms?

• One kilogram is about 2.2 pounds, so divide: 154 ÷ 2.2.
• 154 ÷ 2.2 = 70 kg.
• Check the direction: a kilogram is heavier than a pound, so the number comes down. 70 is smaller than 154 ✓.

The trap: multiplying by 2.2 (154 × 2.2 = 339 kg). Pounds to kilograms is a division.

3. Temperature conversions — Celsius and Fahrenheit both ways

Convert 37 °C to Fahrenheit.

• Multiply by 9: 37 × 9 = 333.
• Divide by 5: 333 ÷ 5 = 66.6.
• Add 32: 66.6 + 32 = 98.6 °F.
• Check: 37 °C is normal body temperature, and 98.6 °F is the familiar reading ✓.

The trap: adding 32 before dividing by 5 (37 + 32 = 69, then × 9 ÷ 5 = 124.2). The multiply-and-divide come first; the + 32 comes last.

4. Rate and time — distance, speed and time in one formula

A delivery van travels at 60 miles per hour for 3.5 hours. How far does it go?

• Use d = rt: distance = rate × time.
• 60 × 3.5 = 210 miles.
• Check the unit: "miles per hour" times "hours" leaves miles ✓.
• Rearranged, the same formula gives time and rate: a 240-mile trip at 80 mph takes t = d ÷ r = 240 ÷ 80 = 3 hours, and 210 miles in 3.5 hours is r = 210 ÷ 3.5 = 60 mph.

The trap: multiplying by a time given in minutes against an hourly rate, or dividing where the formula multiplies. Match the time unit to the rate before you compute.

5. Area and perimeter — square units for area, linear units for perimeter

A rectangle is 12 cm long and 5 cm wide. Find its area and its perimeter.

• Area is length × width: A = 12 × 5 = 60 cm².
• Perimeter adds the four sides: P = 2(12 + 5) = 2 × 17 = 34 cm.
• Check the units: area is in square centimeters, perimeter in plain centimeters. A perimeter answers a distance.
• For a square with side 9, the same idea gives P = 4s = 4 × 9 = 36.

The trap: adding the sides when the question asks for area (12 + 5 = 17), or reporting the area in centimeters. Area is square units; perimeter is linear units.

6. Volume — three lengths multiplied

A storage box is 4 m long, 3 m wide and 2 m high. What is its volume?

• The three lengths are 4 m, 3 m and 2 m.
• Multiply the first two: 4 × 3 = 12.
• Then the third: 12 × 2 = 24 m³.
• Check the unit: three lengths multiplied give a cubic unit ✓.

The trap: adding the three lengths (4 + 3 + 2 = 9) instead of multiplying, or writing the answer in square units. Volume is three lengths, so the unit is cubed.

7. Circumference of a circle — 2πr

A circle has a radius of 7 cm. What is its circumference?

• The radius is 7 cm.
• Use C = 2πr with π ≈ 3.14: 2 × 3.14 = 6.28.
• Then 6.28 × 7 = 43.96 cm.
• Check the unit: a circumference is a distance, so it is in plain centimeters, not square ones.

The trap: using the diameter as the radius, or squaring the radius (that gives area, not circumference). Circumference is 2πr; area is πr².

8. Reading data — the total, and one entry

A step counter logs the week as a table of days and counts: Monday 8,200; Tuesday 9,500; Wednesday 7,800; Thursday 10,000; Friday 9,000. What is the week's total?

• Read each row and add: 8,200 + 9,500 = 17,700.
• Continue: 17,700 + 7,800 = 25,500, and 25,500 + 10,000 = 35,500.
• Add the last day: 35,500 + 9,000 = 44,500 steps.
• A single-row question is read the same way: the highest day is Thursday at 10,000.

The trap: reading the wrong row, or answering a "total" question with a single entry. Name the quantity first; then read only the rows it needs.

9. Mean, median and mode — the average, the middle and the most common

Find the mean and the median of 4, 8, 6, 10, 2.

• Mean is the total divided by the count: 4 + 8 + 6 + 10 + 2 = 30, and 30 ÷ 5 = 6.
• Median needs the values sorted first: 2, 4, 6, 8, 10.
• The middle value is the third: 6. (With an even count, average the two middle values.)
• The mode is the value that appears most often — here every value appears once, so there is no mode.

The trap: reporting the median of an unsorted list, or using the mean when the question asks for the median. Mean uses every value; median only needs the middle after sorting.

10. Range — the largest value minus the smallest

Find the range of 4, 8, 6, 10, 2.

• The largest value is 10 and the smallest is 2.
• Range = largest − smallest = 10 − 2 = 8.
• Check: the spread runs from 2 up to 10, a distance of 8 ✓. (The mean is 30 ÷ 5 = 6 and the median is 6 — neither is the range.)

The trap: reporting the mean (6) or one endpoint (10 or 2) instead of the difference. The range is a single distance: the biggest minus the smallest.

11. The relationship between two variables — increasing, decreasing, or constant

A car's distance is recorded each hour: 0 hours → 0 mi, 1 → 30 mi, 2 → 60 mi, 3 → 90 mi. Describe how distance and time are related, and find the rate of change.

• From 0 h to 3 h the distance climbs 0 → 90 miles: the output rises as the input rises, so this is a positive (increasing) relationship.
• Rate of change = change in output ÷ change in input = (30 − 0) ÷ (1 − 0) = 30 miles per hour.
• Every row adds 30 miles (0, 30, 60, 90), so the rate stays constant at 30 mph — a straight line.
• Because distance ÷ time (30 ÷ 1, 60 ÷ 2, 90 ÷ 3) is always 30, the two are also directly proportional: y ÷ x is the same at every point (y = kx with k = 30).
• If the output fell instead — say 90, 60, 30 — the relationship would be negative (decreasing): one rises as the other falls. A flat 40 at every input would be constant.
• Inversely proportional is a different, specific rule: the product x × y is the same at every point (y = k ÷ x), as in 2 × 12 = 3 × 8 = 4 × 6 = 24. It is not the same as any falling line — a straight-line decrease is a negative relationship, not inverse proportionality.

The trap: calling any falling line "inversely related", or reading the final value (90) as the "rate". A rate of change is the change in one variable divided by the change in the other.

A quick reference — two-variable relationships.

Two specific rules sit inside those: quantities are directly proportional when y ÷ x is the same at every point (y = kx), and inversely proportional when x × y is the same at every point (y = k ÷ x). A straight-line decrease is a negative relationship, not the same as inverse proportionality.

12. The area of a circle — A = πr²

A circle has a radius of 3 m. What is its area?

• The radius is 3 m.
• Use A = πr² with π ≈ 3.14: 3² = 9, then 3.14 × 9 = 28.26 m².
• Check the unit: area is in square meters, not plain meters ✓.
• The circumference of the same circle is 2πr = 2 × 3.14 × 3 = 18.84 m — a distance, not the area.

The trap: using 2πr (the circumference) when the area was asked for, or forgetting to square the radius before multiplying by π. Area is πr²; circumference is 2πr.

The traps, collected

Most wrong answers in this topic's practice items are one of these.

• The wrong unit factor: multiplied where the conversion divides, or divided where it multiplies (2.5 g is 2,500 mg, not 0.0025 mg).
• mL vs L, mg vs g: moved the decimal the wrong number of places.
• kg vs lb swapped: multiplied by 2.2 instead of dividing.
• Mean vs median: averaged a set when the middle value was asked for (or the reverse).
• Called a perimeter an area (or the reverse): square units for area, linear for perimeter.
• Stopped short: gave the unit price or one entry where the question asked for the total.
• Called the spread the center: reported the mean or one endpoint (max or min) when the range — the difference — was asked for.
• Read a rate backwards: gave the final value, or flipped a rate of change (hours per mile for miles per hour).
• Used circumference for area: computed 2πr (a distance) when the question asked for πr² (the area), or forgot to square the radius.

Answer-choice strategies: three moves for when the setup will not come

1. Convert to the answer's unit first. Name the unit the answer needs, put every given quantity into that unit, and the setup writes itself.

How many mL of a 500 mg/mL solution hold 250 mg? The answer is a volume; write the dose over the concentration so mg cancels: 250 ÷ 500 = 0.5 mL.

2. Estimate the size before you compute. A conversion or a rate has a believable size.

60 mph for 3.5 hours is more than 180 miles and less than 240 — a choice of 21 miles or 2,100 miles is gone before you finish multiplying.

3. Carry the units and let them cancel. Write a conversion as a fraction so the unit you do not want cancels and the one you want survives.

154 lb × (1 kg / 2.2 lb): the lb cancels top and bottom, leaving kilograms — 154 ÷ 2.2 = 70 kg.

How to practice this

• Work the free Measurement and data practice set with a pencil, writing every unit out. The unit is where these items set their traps.
• Drill the procedures you get wrong, not the ones you already know. Sorting your errors by procedure beats counting them.
• Read the explanation on every item, including the ones you got right. A right answer reached with the wrong unit comes back on test day.
• Re-attempt what you missed a day later, not immediately: a day later measures whether the method stuck.
• Keep the Numbers and algebra guide beside this one — rates and percents cross between the two topics.

Where to go next

• Next topic — Human anatomy and physiology
• The rest of the section — Numbers and algebra.
• The formula sheet — the formulas and conversions ATI publishes — the conversions and units this topic's items are answered in.

This topic sits inside the Math section and carries ATI's published 11% of the exam and 16 of the section's 34 scored items — the blueprint's own split.

TEAS® is a registered trademark of Assessment Technologies Institute, LLC (ATI). Elk Ridge Academy is an independent study resource and is not affiliated with, endorsed by, or sponsored by ATI.