Question

alice, deepak, and ivan each measure the length of a 6.5-inch pencil five times. they record their measurements as shown. alice’s, deepak’s, and ivan’s work alice: 6.25 in., 6.83 in., 6.11 in., 6.94 in., 6.19 in. deepak: 7 in., 7 in., 6 in., 7 in., 6 in. ivan: 6.5 in., 6.4 in., 6.5 in., 6.5 in., 6.4 in. complete the statements using the drop-down menus. drop-down menu with options alice, deepak, ivan took the most accurate measurements. drop-down menu took the most precise measurements.

Explanation:

• Accuracy: Accuracy refers to how close a measurement is to the true value. The true length of the pencil is \(6.5\) inches.
• For Alice: The values \(6.25\), \(6.83\), \(6.11\), \(6.94\), \(6.19\) are relatively far from \(6.5\).
• For Deepak: The values \(7\) and \(6\) are far from \(6.5\) (average of Deepak's measurements: \(\frac{7 + 7+6 + 7+6}{5}=\frac{33}{5} = 6.6\)).
• For Ivan: The values \(6.5\), \(6.4\), \(6.5\), \(6.5\), \(6.4\) (average of Ivan's measurements: \(\frac{6.5+6.4 + 6.5+6.5+6.4}{5}=\frac{32.3}{5}=6.46\)) are closest to \(6.5\).
• Precision: Precision refers to how close the measurements are to each other.
• Alice's measurements (\(6.25\), \(6.83\), \(6.11\), \(6.94\), \(6.19\)) have a large spread.
• Deepak's measurements (\(7\), \(7\), \(6\), \(7\), \(6\)) have two distinct values with a spread of \(1\) inch.
• Ivan's measurements (\(6.5\), \(6.4\), \(6.5\), \(6.5\), \(6.4\)) have values that are either \(6.4\) or \(6.5\), with a small spread.

Answer:

Ivan took the most accurate measurements. Ivan took the most precise measurements.