Question

studied did not study
88 34
90 67
86 80
96 59
which statements about the data sets are true? check all that apply.
the mean absolute deviation for the group of students who studied is 12.
the mean absolute deviation for the group of students who did not study is 13.5.
the data for the group that studied are more spread out than the data for the group that did not study.
the data for the group that did not study are more spread out than the data for the group that studied.
the data for the group that studied are more clustered around the mean than the data for the group that did not study.
the data for the group that did not study are more clustered around the mean than the data for the group that did

Explanation:

To solve this, we first calculate the mean and mean absolute deviation (MAD) for both groups.

Step 1: Group that Studied (Data: 88, 90, 86, 96)

• Mean (\(\bar{x}\)):

\(\bar{x} = \frac{88 + 90 + 86 + 96}{4} = \frac{360}{4} = 90\)

• MAD:

\(|88 - 90| = 2\), \(|90 - 90| = 0\), \(|86 - 90| = 4\), \(|96 - 90| = 6\)
\(MAD = \frac{2 + 0 + 4 + 6}{4} = \frac{12}{4} = 3\) (Wait, the first option says MAD is 12—this is incorrect. Maybe a miscalculation? Wait, no—wait, maybe the data is different? Wait, no, the table has four rows for "Studied": 88, 90, 86, 96. Wait, maybe I misread. Wait, the user’s table: "Studied" column: 88, 90, 86, 96. "Did Not Study": 34, 67, 80, 59. Wait, no—wait, the table has four rows? Wait, the first row: Studied=88, Did Not Study=34; second: 90, 67; third: 86, 80; fourth: 96, 59. So "Studied" has 4 data points, "Did Not Study" has 4.

Wait, let’s recalculate for "Did Not Study" (Data: 34, 67, 80, 59):

• Mean: \(\frac{34 + 67 + 80 + 59}{4} = \frac{240}{4} = 60\)
• MAD:

\(|34 - 60| = 26\), \(|67 - 60| = 7\), \(|80 - 60| = 20\), \(|59 - 60| = 1\)
\(MAD = \frac{26 + 7 + 20 + 1}{4} = \frac{54}{4} = 13.5\) (so the second option is correct).

Analyzing Spread:

• MAD for "Studied" is 3 (smaller, so more clustered around the mean).
• MAD for "Did Not Study" is 13.5 (larger, so more spread out).

Evaluating Statements:

1. "The mean absolute deviation for the group of students who studied is 12." → False (MAD is 3).
2. "The mean absolute deviation for the group of students who did not study is 13.5." → True (calculated MAD is 13.5).
3. "The data for the group that studied are more spread out than the data for the group that did not study." → False (MAD of "Studied" is smaller).
4. "The data for the group that did not study are more spread out than the data for the group that studied." → True (MAD of "Did Not Study" is larger).
5. "The data for the group that studied are more clustered around the mean than the data for the group that did not study." → True (smaller MAD means more clustered).
6. "The data for the group that did not study are more clustered around the mean than the data for the group that did" → False (larger MAD means less clustered).

Answer:

• The mean absolute deviation for the group of students who did not study is 13.5.
• The data for the group that did not study are more spread out than the data for the group that studied.
• The data for the group that studied are more clustered around the mean than the data for the group that did not study.

(In boxed form for the correct options, assuming the options are labeled as follows—since the original options are checkboxes, we list the true ones:

• The mean absolute deviation for the group of students who did not study is 13.5.
• The data for the group that did not study are more spread out than the data for the group that studied.
• The data for the group that studied are more clustered around the mean than the data for the group that did not study.

If we use the original option labels (assuming the options are, e.g., A to F):

• B. The mean absolute deviation for the group of students who did not study is 13.5.
• D. The data for the group that did not study are more spread out than the data for the group that studied.
• E. The data for the group that studied are more clustered around the mean than the data for the group that did not study.

But based on the calculation, these are the true statements.)