One-variable data

Digital SAT · Math · Problem-Solving and Data Analysis. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

These questions give you one list of numbers and ask you to describe it. Two things matter: where the middle of the data is, and how spread out the data is.

The mean and the median describe the middle. The range and the standard deviation describe the spread. You never have to calculate a standard deviation on the SAT. You only compare: values packed close to the mean give a small standard deviation, and values far from the mean give a large one.

An outlier is a value far from the rest. It pulls the mean toward itself and makes the range and standard deviation larger, but it hardly moves the median.

Rules to remember

Common mistake

Finding the median without first putting the values in order, or taking the middle row of a frequency table instead of counting to the middle value. Always order the data and count positions.

Worked example

The mean of a list of 6 numbers is 15. Two of the numbers, 9 and 11, are removed. What is the mean of the remaining 4 numbers?

  1. Sum of the 6 numbers = 15 × 6 = 90.
  2. Sum after removing two numbers = 90 − 9 − 11 = 70.
  3. New mean = 70 ÷ 4 = 17.5.

Answer: 17.5

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