Identify outliers and describe their effect on measures of center and spread.
Free, timed SHSAT practice sets on outliers & their effect— every question includes a full worked explanation, and there's no account required.
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An outlier is a value far away from the rest of the data. To see its effect, compute each measure with and without it.
Example: 4, 5, 5, 6, 30. The outlier is 30.
So an outlier pulls the mean and the range strongly, but the median only a little.
Common traps: when you remove the outlier, subtract it from the sum and reduce the count by 1. If the question asks how much a measure changes, give the difference, not the new value.
The other prices all lie between $35 and $47, near $41. $100 is far from all of them, so it is the outlier. An outlier is a value that lies unusually far from the rest of the data. (Picking the lowest price, which is at the far end from the outlier, gives $35. Picking the highest of the clustered prices gives $47. Picking the middle price of the cluster gives $42.)
Removing $131 leaves 5 donations summing to 225. New mean = 225 \(\div\) 5 = 45. (Reporting the median of the remaining donations gives 46. Removing $131 from the sum but still dividing by 6 (\(225 \div 6\)) gives 37.5. Leaving the outlier in (\(356 \div 6\)) gives about 59.33.)
With the outlier, range = 105 \(-\) 43 = 62. Without it, range = 61 \(-\) 43 = 18. Decrease = 62 \(-\) 18 = 44. (Reporting the outlier score itself gives 105. Stopping at the new range gives 18. Reporting the range with the outlier gives 62.)