The Life Starter
Sign up
Grade 9 · unit review

Review: Algebra1: Descriptive Data and Outliers

Data summaries describe center and spread using stated definitions. Mean, median, interquartile range and mean absolute deviation respond differently to extreme values, so the chosen measure should match the question and convention.

Download reviews and answer keys

Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. For the complete supplied data [7, 8, 9, 10, 21], which pair is (mean, median)?
Need a hint?
  • A mean divides the total by the number of values.
  • Sort before finding the median and count every value in the mean denominator.
2. For sorted data [8, 15, 22, 29, 36, 43], use the median of each three-value half for Q1 and Q3. Find IQR.
Need a hint?
  • Interquartile range subtracts the lower quartile from the upper quartile.
  • Quartile conventions can differ across software and sample sizes.
3. For data [7, 14, 21], find mean absolute deviation from the mean, exactly.
Need a hint?
  • Mean absolute deviation averages each value’s nonnegative distance from the mean.
  • Use the mean of the data before computing distances.
4. Data 7,8,9,10,11 change only by replacing the largest value with 51. Which statement is true?
Need a hint?
  • Replacing one endpoint of a sorted data set can increase the total without changing the middle value.
  • An unchanged median does not mean the data did not change.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. For the complete supplied data [9, 10, 11, 12, 23], which pair is (mean, median)? Candidate answers: (A) (11, 13) (B) (13, 11) (C) (13, 12) (D) (23, 11). 2. For sorted data [10, 19, 28, 37, 46, 55], use the median of each three-value half for Q1 and Q3. Find IQR. Candidate answers: (A) 18 (B) 27 (C) 45 (D) 9. 3. For data [9, 18, 27], find mean absolute deviation from the mean, exactly. Candidate answers: (A) 0 (B) 18 (C) 6 (D) 9. 4. Data 9,10,11,12,13 change only by replacing the largest value with 63. Which statement is true? Candidate answers: (A) Both mean and median stay the same (B) The mean decreases (C) The mean increases; the median stays the same (D) The median increases by 50.

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. (13, 11). The sum is 65; divide by 5 to get mean 13. The third sorted value is the median 11. The high value pulls the mean upward. 2. 27. Q1 is the lower-half middle value 19; Q3 is the upper-half middle 46. Thus IQR=46−19=27, under the stated convention. 3. 6. The mean is 18. Absolute distances are 9,0,9. Their average is (9+0+9)/3=6; signed distances would incorrectly cancel. 4. The mean increases; the median stays the same. The sum increases by 50, so the mean increases by 50/5=10. The middle sorted value remains 11. The outlier affects these centers differently.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.