The prices of 7 race cars are 126,000 140,000 140,000 180,000 400,000 400,000 819,000 The mean is $315,000?
the median is 180,000
which of these measures of central tendency best represents the value of the seven race cars and why??
Both the median and mean values are correct. The mean is usually a more meaningful because it is the average car sales price. It will give you the minimum average error when comparing the price of a car selected at random.
I think the median is better because the 819,000 skews the mean high. We could argue about this for quite a while :)
The median, which is 180,000, best represents the value of the seven race cars.
The reason is that the median is not affected by outliers, while the mean can be skewed by extreme values such as the highest priced race car in this case, which is 819,000.
By using the median, we are able to find the middle value when the data is arranged in ascending order, disregarding any extreme values that might not be representative of the overall data set.
To determine which measure of central tendency best represents the value of the seven race cars, we need to understand what each measure represents and evaluate how it relates to the given data.
The three common measures of central tendency are mean, median, and mode:
1. Mean: It is calculated by adding up all the values and dividing the sum by the total number of values. In this case, the mean of the given data is $315,000. The mean provides an average value for the data set by considering all the values equally.
2. Median: The median is the middle value when the data set is arranged in ascending or descending order. In this case, the median is $180,000. The median is not affected by extreme values and can provide a representative value when there are outliers.
3. Mode: The mode is the value or values that appear most frequently in the data set. In this case, there is no mode since no value appears more than once.
Considering the given data set of race car prices, we can see that the prices vary significantly. The presence of higher-priced race cars, such as $400,000 and $819,000, affects the overall average (mean) and may not accurately represent the value of the majority of the race cars.
In this situation, the median ($180,000) is a better measure of central tendency because it is not influenced by outliers and represents the middle value of the data set. Since the majority of the race cars fall below the median price, it is a better indicator of the typical value in this case.
Therefore, the median is the measure of central tendency that best represents the value of the seven race cars in this data set.