To determine which of the three measures (mode, mean, or median) gives the best idea of the typical size of the numbers in the list, we need to understand what each measure represents and how they are affected by the distribution of the data.
1. Mode: The mode is the number that appears most frequently in a data set. In this case, the mode is 2 because it appears three times, more than any other number. However, the mode does not always provide a good representation of the typical value, especially when the data has outliers or when the mode is not near the center of the data.
2. Mean: The mean is the average of all the numbers. It is calculated by summing all the numbers and then dividing by the count of the numbers. The given mean of this data set is 10. But means can be misleading in the presence of outliers or skewed data. In this scenario, the large value of 60 is an outlier and significantly increases the mean, potentially giving a false impression of the typical data value.
3. Median: The median is the middle number when the data is ordered from smallest to largest. If there is an even number of observations, the median is the average of the two middle numbers. In this case, the median is 7, which means when the data is sorted, 7 is the middle value that separates the higher half from the lower half of the data.
To find out which measure provides the best idea of the typical size, we should look at each of them within the context of this data set. The mode of 2 appears to be significantly lower than most of the other numbers, except for the outliers (2 itself and 60). The mean of 10 is skewed by the outlier 60. The median of 7, however, lies towards the center of the majority of the data points without being affected by the outlier.
Therefore, the median is often the best measure of central tendency when dealing with skewed data or when outliers are present. Since it is unaffected by extremely large or small values, it provides a more accurate representation of the typical value in the data set.
For the given data set, the median provides the best idea of the typical size of the numbers in the list.
The correct answer is:
○ A. Median
