Z-Score and the Empirical Rule: Background You’ll Need 4

Now let’s spend some time understanding how and in what way these kinds of calculations can go wrong.

Identifying Calculation Mistakes

Suppose the statistician making these calculations thought she was using her calculator correctly, but in three different attempts, she arrived at three different answers. The three potential answers to her computational problem are shown below in Questions 9, 10, and 11 rounded to the nearest hundredth. For each, decide if it was computed correctly or, if not, explain what went wrong. Please refer to the Order of Operations Student Resource as needed.

Interactive example

When making complicated calculations involving order of operations, your calculator can be a friend or a foe. Some of the most commonly occurring mistakes come from not using parentheses to wrap up operations that need to occur first. Dropped negatives and mislabeled units are also common culprits. You’ll be presented with questions below that may include any of these tricky spots. Let’s practice a bit before moving on.

Both of the questions below have mistakes. What are they?

  1. [latex]\dfrac{15-12}{4}=12[/latex]
  2. [latex]\dfrac{7-9}{8}=\dfrac{1}{4}[/latex]

Now it’s your turn to try finding the mistakes. Some of the questions below may have a mistake, and some may not.

question 9

question 10

question 11

Questions 12, 13, and 14 below show three potential answers to a similar computational problem, rounded to the nearest hundredth. This time, the units of measure are included. For each, decide if it was computed correctly or, if not, explain what went wrong.

question 12

question 13

question 14

Now that you’ve had some practice making these calculations and learning how they can go wrong, it’s time to move on to the next section.