Final answer:
When calculating outliers using the interquartile range (IQR) for the given home prices, we found that none of the prices fall outside the accepted range to be classified as an outlier, although the highest price may seem unusually large in comparison to the others.
Step-by-step explanation:
To determine the outlier among the given home prices, we first need to calculate the interquartile range (IQR). Observing the list of prices: $161,000, $173,000, $184,000, $159,000, and $1,230,000, we notice that one value is significantly higher than the rest. To find potential outliers we follow these steps:
- Arrange the prices in ascending order: $159,000, $161,000, $173,000, $184,000, $1,230,000.
- Find the median (second quartile), which is $173,000 given that it is the middle number.
- Identify the first quartile (Q1) and third quartile (Q3). Given that we have only five data points, we will consider the smallest value as Q1 and the largest value as Q3 in this specific case.
- Compute the IQR: IQR = Q3 - Q1 = $1,230,000 - $159,000 = $1,071,000.
- Calculate the lower bound (Q1 - 1.5*IQR) and upper bound (Q3 + 1.5*IQR). However, since the smallest price is not going to be considered an outlier from the downside, we only need to calculate the upper bound: $1,230,000 + 1.5*$1,071,000 = $1,230,000 + $1,606,500 = $2,836,500.
- Any value above the upper bound is an outlier. In this case, since all prices except the highest are below $2,836,500, there are no outliers on the upper side too.
Therefore, based on this approach, there are no outliers among the given set of home prices. However, it is worth mentioning that in practice, the value of $1,230,000 seems remarkably higher than the other prices, and in a more in-depth analysis, it could indeed be considered an outlier. Yet, by our calculation, no prices fall outside the accepted range for outliers.