Pregunta
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(a) Ashley wants to determine which letter appears the most often in her favorite poem. Which measure should she use? \[ \text { Mean } \] (b) At a certain company, the 9 employees have the following weekly salaries: \( \$ 570, \$ 800, \$ 810, \$ 830, \$ 840, \$ 860, \$ 870, \$ 920, \$ 950 \). Which measure should be used to summarize the data? Mean Median (c) The last 9 calls to a customer support line had the following lengths (in minutes): \( 22,23,24,25,26,27,28,30,31 \). Which measure should be used to summarize the data? Mean Median

Ask by Bowman Erickson. in the United States
Mar 12,2025

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**(a) Mode** **(b) Median** **(c) Mean**

Solución

**(a) Determining the most frequent letter in a poem** Ashley is interested in which letter appears the most often. To find the most frequent occurrence in a dataset (or a set of letters), the appropriate measure is the **mode**. The mode is defined as the value that appears most frequently. \[ \text{Mode} = \text{Value with highest frequency} \] --- **(b) Summarizing the weekly salaries** The nine weekly salaries are: \[ \$570,\ \$800,\ \$810,\ \$830,\ \$840,\ \$860,\ \$870,\ \$920,\ \$950 \] When summarizing salary data, especially when one or more values are significantly different from the rest (an outlier, like \$570 in this case), the median is typically preferred to prevent the outlier from skewing the result. The median is the middle value when the data are ordered from least to greatest. Given there are 9 values, the 5th number is the median. Here, the median salary is: \[ \$840 \] Thus, the median is the more appropriate measure. --- **(c) Summarizing the call length data** The nine call lengths (in minutes) are: \[ 22,\ 23,\ 24,\ 25,\ 26,\ 27,\ 28,\ 30,\ 31 \] Since the data does not appear to have any extreme outliers and is relatively symmetric, the mean is a suitable summary measure. The mean is computed by adding all the values and dividing by the number of observations. \[ \text{Mean} = \frac{22 + 23 + 24 + 25 + 26 + 27 + 28 + 30 + 31}{9} \] Thus, in this scenario, the mean gives a good representation of the typical call length. --- **Final Answers:** (a) **Mode** (b) **Median** (c) **Mean**

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To determine which letter appears the most often in her favorite poem, Ashley should use the mode. The mode is the value that occurs with the highest frequency, making it perfect for identifying which letter is the reigning champ in her poetic masterpiece! Regarding the salaries of the 9 employees, using the median would be the best measure to summarize the data. The median provides a better representation of the central tendency when there may be outliers, as it positions itself right in the middle of the sorted salaries, helping illustrate the typical employee wage more accurately than the mean. When analyzing the last 9 calls to a customer support line, the median is again the ideal choice for summarizing the data. Given the relatively small and consistent range of call lengths, the median captures the point at which half of the calls are shorter and half are longer, providing a clearer picture of the typical call duration without being swayed by any potential outliers.

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