Fundraiser Means, Medians, and an Outlier Bulk Order
Two sixth-grade classes track daily sales for a five-day wrapping-paper fundraiser. Class A’s daily totals are $120, $135, $128, $132, and $410; the $410 day came from one parent’s office bulk order. Class B’s daily totals are $180, $190, $175, $185, and $170. The principal will announce the class with the higher “average daily sales” and award a pizza party. Class B’s teacher objects that Class A’s average is distorted by a single unusual day and that the median is a fairer summary. The student council must decide whether to use the mean or the median and whether the pizza party should go to Class A, Class B, or neither with the current data. They also want a one-sentence justification that can be read aloud without using formulas.
1. Compute the mean and median daily sales for each class.
Read the worked answer
Class A total = 120 + 135 + 128 + 132 + 410 = 925. Mean = 925 ÷ 5 = 185. Ordered values: 120, 128, 132, 135, 410; the median is the middle value, 132. Class B total = 180 + 190 + 175 + 185 + 170 = 900. Mean = 900 ÷ 5 = 180. Ordered values: 170, 175, 180, 185, 190; the median is 180. So by mean, Class A leads 185 to 180; by median, Class B leads 180 to 132.
2. Explain why Class A’s mean and median differ so much, and identify which measure better represents a typical day for Class A.
Read the worked answer
Class A’s $410 day is far above the other four days, which range from $120 to $135. The mean uses every dollar, so that one bulk order pulls the average up: without it, the other four days total $515 and average $128.75. The median ignores the size of the extreme value and stays at $132, close to the typical day. For Class A, the median is the better measure of a typical daily sale because the distribution is strongly skewed by one unusual event. Class B has no such outlier; its mean and median are both $180.
3. Recommend how the student council should award the pizza party, and give a one-sentence justification suitable for reading aloud.
Read the worked answer
The decision depends on the stated rule. If “average daily sales” means the mean, Class A wins narrowly, 185 to 180. If the goal is a typical day or consistency, Class B wins because its median is 180 versus Class A’s 132 and its daily sales are tightly clustered. A defensible recommendation is to award the pizza party to Class B for consistent daily sales, while separately recognizing Class A for the highest total funds raised ($925 vs. $900). Read-aloud justification: “Class A had one huge day, but Class B was stronger on a typical day, so we are comparing medians rather than letting one bulk order decide the prize.”