Question

which data set would the mean be significantly affected by extreme values, making the median a more reliable measure of center?
earnings from a school car wash fundraiser by five students: $50, $55, $57, $60, $50.
money earned from babysitting by five students: $30, $32, $33, $35, $330.
tips earned by five students working as servers: $20, $22, $23, $25, $25.
profits from selling handmade crafts online by five students: $40, $42, $43, $45, $40.

Explanation:

Step1: Calculate the mean and median for each data set

• Earnings from a school car wash fundraiser:
• Data: \(50,55,57,60\)
• Mean: \(\frac{50 + 55+57+60}{4}=\frac{222}{4} = 55.5\)
• Median: Arrange data \(50,55,57,60\). Median=\(\frac{55 + 57}{2}=56\)
• Money earned from babysitting:
• Data: \(30,32,33,35\)
• Mean: \(\frac{30+32 + 33+35}{4}=\frac{130}{4}=32.5\)
• Median: Arrange data \(30,32,33,35\). Median=\(\frac{32+33}{2}=32.5\)
• Tips earned by servers:
• Data: \(20,22,23,25,25\)
• Mean: \(\frac{20+22 + 23+25+25}{5}=\frac{115}{5}=23\)
• Median: Arrange data \(20,22,23,25,25\). Median = 23
• Profits from selling handmade crafts:
• Data: \(40,42,43,45\)
• Mean: \(\frac{40+42+43+45}{4}=\frac{170}{4} = 42.5\)
• Median: Arrange data \(40,42,43,45\). Median=\(\frac{42+43}{2}=42.5\)

Step2: Analyze the effect of extreme values

• For the "Earnings from a school car wash fundraiser" data set, if we assume a normal distribution of similar - valued data (most values around \(50 - 57\)), the value \(60\) is relatively an extreme value.
• The mean \(\bar{x}=55.5\) is affected by the \(60\) (since \(\frac{50 + 55+57}{3}=\frac{162}{3}=54\)). The median is less affected.

Answer:

Earnings from a school car wash fundraiser.