Here are the prices (in thousands) for 9 houses for sale in a local neighborhood: $160, $295, $298, $299, $300, $302, $308, $312, $314
Which measure should be used to summarize the data?
A. mean B. Median C. Mode
Please help!
I think it might be B.
The mean will be skewed downward by that $160 outlier. All of the other prices lie near $300, so I'd go with the median value.
Since no price occurs more than once, the mode is useless.
To summarize the data for the prices of the houses, you can use either the mean, median, or mode.
The mean is the average of the numbers and is found by adding up all the values and dividing by the total number of values.
The median is the middle value when the data is arranged in ascending or descending order.
The mode is the value that appears most frequently in the data set.
In this case, since you are looking for a measure that gives a central tendency, the correct choice would be the median (B).
To determine which measure to use to summarize the data, you need to consider the characteristics of the data set.
The mean is the average of a set of numbers and is calculated by summing up all the numbers and dividing by the total count. It is a good measure to use when there are no extreme outliers and the data is approximately normally distributed.
The median is the middle value of a data set when it is arranged in ascending or descending order. It is not affected by extreme outliers and is a better measure when the data set contains extreme values.
The mode is the value that appears most frequently in a data set. It is useful when you want to determine the most common value in the data set.
In this case, the data set consists of house prices. While the mean is a valid measure to consider, it can be influenced by extreme values. Looking at the prices given, we see that $160 and $314 are the lowest and highest values respectively, and the rest of the prices are clustered around the middle.
To summarize the data, it would be more appropriate to use the median (option B) as it would provide a better representation of the central tendency of the prices, taking into account the extreme outliers.
Therefore, you are correct in selecting option B (median) as the measure to summarize the data.