Skip to content

Menu

ExamPassoLog in

ATI TEAS: Measurement and Data Concepts

Importance ★★★★★ · 47% (estimate)

Overview

This chapter covers measuring and describing things with numbers. You will read tables and graphs, find the mean, median, mode, and range of a data set, spot outliers, convert between U.S. customary and metric units, and find perimeter, area, and volume of basic shapes.

The mean is the average: add all the values and divide by how many there are. The median is the middle value after the data are put in order, and the mode is the value that appears most often. For the data 2, 3, 3, 4, 8, the mean is 20 divided by 5, which is 4, while the median and the mode are both 3. The single high value of 8 is an outlier, and it pulls the mean up but barely moves the median, while the range (highest value minus lowest) shows how spread out the data are.

For unit conversions, multiply by a conversion factor so that the unwanted unit cancels out. Common factors include 1 inch = 2.54 centimeters, 1 kilogram is about 2.2 pounds, and 1 liter = 1,000 milliliters. Perimeter is the distance around a shape, area is the space it covers in square units, and volume is the space it fills in cubic units.

Key concepts

  • Mean

    The average of a data set: add all the values and divide by the number of values. For 2, 3, 3, 4, 8 the mean is 20 / 5 = 4.

    Memory tipMean = sum / count. Outliers pull it toward them.

  • Median

    The middle value when the data are in order. With an even number of values, it is the mean of the two middle values. For 2, 3, 3, 4, 8 the median is 3.

    Memory tipSort first, then find the middle.

  • Mode

    The value that appears most often. A data set can have no mode, one mode, or more than one. For 2, 3, 3, 4, 8 the mode is 3.

    Memory tipMode = most often.

  • Range

    The difference between the largest and smallest values, showing how spread out the data are. For 2, 3, 3, 4, 8 the range is 8 - 2 = 6.

    Memory tipRange = max - min.

  • Outlier

    A value far away from the rest of the data. An outlier pulls the mean toward it but has little effect on the median.

    Memory tipWith an outlier, the median describes the typical value better.

  • Metric conversions

    Exact or standard factors: 1 inch = 2.54 cm, 1 kg is about 2.2 lb, 1 L = 1,000 mL, 1 kg = 1,000 g, 1 m = 100 cm.

    Memory tipSet up the factor so the unit you want to remove cancels.

    Source: NIST (U.S. customary/metric conversion) · as of 2024

  • Perimeter, area, volume

    Perimeter is the distance around a shape (rectangle: 2l + 2w). Area is the surface covered (rectangle: l x w; circle: pi x r squared). Volume is the space inside (box: l x w x h).

    Memory tipPerimeter in units, area in square units, volume in cubic units.

See it in a picture

Dot plot on a number line from 0 to 10 showing 2, 3, 3, 4, 8, with two dots stacked at 3. A triangle under 3 is labeled Median = 3 and one under 4 is labeled Mean = 4. The dot at 8 is labeled Outlier. Text above: Mean = 20 ÷ 5 = 4, Median = 3, Mode = 3.
For 2, 3, 3, 4, 8, the median (middle value) is 3, but one high outlier (8) pulls the mean up to 4.

Often tested

  • Always sort the data before finding the median.
  • One very high or very low value changes the mean much more than the median.
  • When converting from a larger unit to a smaller one, the number gets bigger (2 m = 200 cm).
  • Read graph titles, axis labels, and scales before choosing an answer.

Easy to confuse: Mean, median, and mode

MeasureHow to find itFor 2, 3, 3, 4, 8
MeanAdd all values, divide by the count20 / 5 = 4
MedianMiddle value after sorting3
ModeMost frequent value3

3 sample questions

Verified practice questions from this unit.

Practice questionReviewedMathematics › Measurement and Data★★★★★

Question 1. What is the mean of this data set? 3, 9, 4, 10, 4

  1. ① 4
  2. ② 6
  3. ③ 7
  4. ④ 30
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ② 6

Key point: Mean = sum ÷ number of values

The mean (average) is the sum divided by how many values there are.

  1. Sum: 3 + 9 + 4 + 10 + 4 = 30
  2. Count: 5 values
  3. Mean: 30 ÷ 5 = 6

Check: 6 × 5 = 30.

Wrong choices

  • 4: 4 is the median and the mode, not the mean.
  • 7: 7 is the range (10 − 3).
  • 30: 30 is the sum; you still need to divide by 5.
Practice questionReviewedMathematics › Measurement and Data★★★★★

Question 2. What is the median of this data set? 12, 7, 15, 9, 20, 11

  1. ① 11.5
  2. ② 12
  3. ③ 11
  4. ④ About 12.3
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ① 11.5

Key point: Median: order the data; average the two middles if even

Put the data in order first, then find the middle.

  1. In order: 7, 9, 11, 12, 15, 20
  2. There are 6 values, so the two middle values are 11 and 12.
  3. Median = (11 + 12) ÷ 2 = 11.5

Check: three values (7, 9, 11) are below 11.5 and three (12, 15, 20) are above.

Wrong choices

  • 12: This picks a middle number without putting the data in order first.
  • 11: With an even number of values, the median is the average of the two middle values.
  • About 12.3: This is the mean (74 ÷ 6), not the median.
Practice questionReviewedMathematics › Measurement and Data★★★★★

Question 3. How many grams are in 3.5 kilograms?

  1. ① 3,500 g
  2. ② 350 g
  3. ③ 35,000 g
  4. ④ 0.0035 g
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ① 3,500 g

Key point: 1 kg = 1,000 g; big unit → small unit, multiply

"Kilo" means 1,000, so 1 kg = 1,000 g. Going from a bigger unit to a smaller unit, multiply.

  1. 3.5 × 1,000 = 3,500 g

Check: 3,500 ÷ 1,000 = 3.5 kg.

Wrong choices

  • 350 g: This multiplies by 100; 1 kilogram is 1,000 grams.
  • 35,000 g: This multiplies by 10,000.
  • 0.0035 g: This divides by 1,000 instead of multiplying.
Practice 5 questions from this unit →

AI-written · Verified · Written by AI. Only units that passed a separate AI check (re-reading facts and numbers) are published. Tell us if you find a mistake.