Let's answer each question step-by-step:
### (a) House Prices:
Here are the prices (in thousands) for 9 houses for sale in a local neighborhood: [tex]$293, $[/tex]295, [tex]$300, $[/tex]301, [tex]$303, $[/tex]305, [tex]$308, $[/tex]312, [tex]$471.
To decide which measure to use to summarize the data, we need to consider whether there are any outliers. An outlier is a value that is significantly higher or lower than the other values in the data set.
In this case, the price $[/tex]471 is much higher than the other house prices, making it an outlier. When there is an outlier in the dataset, using the mean can be misleading because it can be skewed by the extreme value.
Therefore, the median would be a better measure to summarize the data for house prices because it is not affected by outliers.
### (b) Favorite Animals:
The readers of a children's magazine are asked to name their favorite animals.
The measure that indicates the animal chosen most often is the one that shows the frequency of each option. This is known as the mode.
Therefore, the measure that indicates the animal chosen most often is the mode.
### (c) Shoe Prices:
The 10 members of the dance team each bought new shoes. Here are the prices they paid: [tex]$51, $[/tex]53, [tex]$54, $[/tex]55, [tex]$57, $[/tex]59, [tex]$60, $[/tex]63, [tex]$64, $[/tex]65.
To determine which measure to use to summarize the shoe prices, we observe that there are no significant outliers in the dataset. The prices are relatively close to each other.
In this case, the mean would be a good measure to summarize the data because it considers all values and gives a central tendency of the dataset.
In summary:
(a) For the house prices, the median should be used to summarize the data.
(b) For the favorite animals, the measure that indicates the animal chosen most often is the mode.
(c) For the shoe prices, the mean should be used to summarize the data.
