Coach Hart calculated the mean, median, mode, and range for these data. He realized he forgot to include Louise’s 11 catches in the table. If he now includes Louise’s 11 catches with the data for the other five players, which of the following measures of center would change from his original calculations?
maybe none of them, depending on the actual data added.
To determine which measures of center would change when Louise's 11 catches are included, we need to consider the mean, median, mode, and range.
1. Mean: The mean is calculated by summing all the values and then dividing by the number of values. Since Louise's 11 catches were not included in the original calculations, the total sum and the number of values used in the calculation were different. Therefore, the mean will change when Louise's catches are included.
2. Median: The median is the middle value when the data is arranged in ascending or descending order. Adding Louise's 11 catches could potentially change the position of the middle value, thus changing the median.
3. Mode: The mode is the value or values that appear most frequently in the data set. If none of the other values were repeated as the mode, including Louise's 11 catches would introduce a new value that appears more frequently than any other, thus changing the mode.
4. Range: The range is the difference between the highest and lowest values in the data set. Adding Louise's 11 catches would potentially increase the highest value, leading to an increase in the range.
Therefore, the measures of center that would change when Louise's 11 catches are included are the mean, median, mode, and range.
To determine which measures of center would change after including Louise's 11 catches, let's first understand what each measure represent:
1. Mean: The mean is the average of a set of numbers. It is calculated by summing up all the values and dividing it by the total number of values.
2. Median: The median is the middle value of a set of numbers when they are arranged in ascending or descending order. If there is an even number of values, the median is calculated by taking the average of the two middle values.
3. Mode: The mode is the value or values that appear most frequently in a set of numbers. A set can have no mode, one mode (unimodal), or multiple modes (multimodal).
4. Range: The range is the difference between the highest and lowest values in a set of numbers.
Considering these measures, including Louise's 11 catches will only impact the mean and range, while the median and mode will remain unaffected.
Explanation for each measure of center:
1. Mean: Including Louise's 11 catches will affect the mean because it takes into account all the values in the data set. As the mean is calculated by summing up all the values and dividing by the total number of values, adding 11 to the sum will change the mean.
2. Median: The median only considers the middle value(s) of the data set. Since Louise's 11 catches will be added to the highest end of the data set, it will not affect the median.
3. Mode: The mode is determined by the most frequently occurring value(s) in the data set. Adding Louise's 11 catches does not change the frequency distribution of the existing values, so the mode will remain the same.
4. Range: Including Louise's 11 catches will affect the range because the highest value of the data set will change. If Louise's catches are higher than any of the existing values, the range will increase; otherwise, it might remain the same.
In summary, the mean and range will change when Coach Hart includes Louise's 11 catches, while the median and mode will remain the same.