Questions: Suppose the list below shows how many text messages Elyse sent each day for the last 10 days. If Elyse wants to know how many text messages she typically sends each day, which measure of central tendency better describes the typical number of text messages per day? 21 22 24 26 26 29 32 32 33 88 Choose the correct answer below. A. Mean; The mean of 333 is a better representative of the typical number of texts since it includes all the data values in its computation. The median of 27.5 is not affected by the most extreme value of 88 texts and is therefore not representative of the typical number of texts. B. Median; The median of 27.5 is a better representative of the center since it is resistant to the one extreme value. The mean of 33.3 is not representative of the typical number of texts since only one number is larger than the mean C. Median, The median of 27.5 is a better representative of the typical number of texts since it divides the bottom 50% of the data values from the top 50% of the data values. The mean is too resistant to the highest value of 88 texts, D. Mean, The mean of 33.3 is a better representative of the typical number of texts since it is higher than the median of 27.5.

Solution Steps

To determine which measure of central tendency better describes the typical number of text messages Elyse sends each day, we need to calculate both the mean and the median of the given data set. The mean is the average of all the numbers, while the median is the middle value when the numbers are sorted in order. We will then compare these values to decide which one is more representative, considering the presence of an outlier (88).

To find the mean, sum all the text messages and divide by the number of days. The sum of the messages is \(21 + 22 + 24 + 26 + 26 + 29 + 32 + 32 + 33 + 88 = 333\). The number of days is 10. Therefore, the mean is:

\[ \text{Mean} = \frac{333}{10} = 33.3 \]

To find the median, first sort the list of messages, which is already sorted as \([21, 22, 24, 26, 26, 29, 32, 32, 33, 88]\). Since there are 10 numbers (an even number), the median is the average of the 5th and 6th numbers in the sorted list:

\[ \text{Median} = \frac{26 + 29}{2} = \frac{55}{2} = 27.5 \]

The mean is \(33.3\) and the median is \(27.5\). The presence of the outlier \(88\) skews the mean higher than most of the data points, while the median remains unaffected by this extreme value. Therefore, the median is a better measure of central tendency in this case because it is resistant to the outlier.

Final Answer