Question

a realtor is displaying the histogram below, which summarizes the percentage of appreciation in value (over the past five years) for each of a sample of 21 houses in newburg park. based on the histogram, estimate the mean appreciation (in percent) for the houses sampled. carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.

Explanation:

Step1: Find the mid - point of each class interval

The class intervals (assuming width of 10, starting from 0 - 10, 10 - 20, 20 - 30, 30 - 40, 40 - 50) have mid - points:
For \(0 - 10\): \(\frac{0 + 10}{2}=5\)
For \(10 - 20\): \(\frac{10+20}{2}=15\)
For \(20 - 30\): \(\frac{20 + 30}{2}=25\)
For \(30 - 40\): \(\frac{30+40}{2}=35\)
For \(40 - 50\): \(\frac{40 + 50}{2}=45\)

Step2: Calculate the sum of \((\text{mid - point}\times\text{frequency})\)

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Step3: Calculate the total frequency

\(n=2 + 3+6+7+3=21\)

Step4: Calculate the mean

The formula for the mean of a grouped data is \(\bar{x}=\frac{\sum_{i = 1}^{k}x_{i}f_{i}}{\sum_{i = 1}^{k}f_{i}}\), where \(x_{i}\) is the mid - point and \(f_{i}\) is the frequency.
\(\bar{x}=\frac{585}{21}\approx27.9\)

Answer:

\(27.9\)