Coach Hart calculated the mean, median, mode, and range for these data. He realized that he forgot to include Louise's 11 catches in the table. If Coach Hart now includes Louise's data with the data for the other five members, which of the following statistical measures would change from his original calculations?
To determine which statistical measures would change after including Louise's data, we need to know the original calculations made by Coach Hart for the mean, median, mode, and range. Please provide the original calculations for each statistical measure.
To determine which statistical measures would change when including Louise's data, let's first understand the definitions of mean, median, mode, and range.
1. Mean: The mean is the average value of a set of numbers. To calculate the mean, you sum up all the values and then divide the sum by the total number of values.
2. Median: The median is the middle value in a set of numbers when they are arranged in ascending or descending order. If there is an even number of values, the median is the average of the two middle values.
3. Mode: The mode is the value(s) that appear most frequently in a set of numbers. A set of numbers can have no mode, one mode (unimodal), or multiple modes (multimodal).
4. Range: The range is the difference between the maximum and minimum values in a set of numbers. It measures the spread or variation of the data.
Now, let's consider the effect of including Louise's data on these statistical measures:
1. Mean: Including Louise's data would change the mean because it involves recalculating the average with her 11 catches. The sum of all catches would increase, and dividing by the new total number of values would result in a different mean.
2. Median: Including Louise's data may or may not change the median. It depends on the position of her 11 catches in the ordered data set. If her catches fall in the middle of the data, then the median would change. Otherwise, the median would remain the same.
3. Mode: Including Louise's data may or may not change the mode. If her 11 catches become the most frequent value(s) in the set, then the mode would change. If there was already a different mode before including her data, then the mode would remain the same.
4. Range: Including Louise's data would potentially change the range, as it would add a new value to the data set. The difference between the maximum and minimum values would likely be different than before.
In summary, the statistical measures that would potentially change from Coach Hart's original calculations are the mean, median, mode, and range. The specific changes would depend on the values of Louise's data and their positions in relation to the existing data.