Even on a crucial examination, students tend to lose focus...

Even on a crucial examination, students tend to lose focus while writing their tests. In a psychology experiment, 20 students were given a 10-minute quiz and the number of seconds they spent'on task'were recorded. Here are the results: $$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline 350 & 380 & 500 & 460 & 480 & 400 & 370 & 380 & 450 & 530 \\\hline 520 & 460 & 390 & 360 & 410 & 470 & 470 & 490 & 390 & 340 \\\hline\end{array}$$ Find the mean and median of the time spent on task. If you were writing a report to describe these times, which measure of central tendency would you use and why?

Even on a crucial examination, students tend to lose focus while writing their tests. In a psychology experiment, 20 students were given a 10-minute quiz and the number of seconds they spent'on task'were recorded. Here are the results:
$$\begin{array}{|c|c|c|c|c|c|c|c|c|c|}\hline 350 & 380 & 500 & 460 & 480 & 400 & 370 & 380 & 450 & 530 \\\hline 520 & 460 & 390 & 360 & 410 & 470 & 470 & 490 & 390 & 340 \\\hline\end{array}$$
Find the mean and median of the time spent on task. If you were writing a report to describe these times, which measure of central tendency would you use and why?

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Key Concepts

Median

The median is the middle value in an ordered data set, which divides the data into two equal halves. It is a measure of central tendency that is particularly informative when the data distribution is skewed or contains outliers, as it is not affected by extreme values.

Mean

The mean is the arithmetic average of a set of numbers, calculated by summing all the values and dividing by the number of observations. It is a commonly used measure of central tendency that provides a simple overall average and is useful when the data distribution is symmetric and free of extreme outliers.

Measures of Central Tendency

Measures of central tendency, including the mean and median, provide summary statistics that describe the center of a distribution. They help in understanding the typical value within a dataset and are foundational concepts in descriptive statistics, guiding how data is reported and interpreted.

Robustness to Outliers

Robustness to outliers refers to a measure's ability to remain representative of the data despite the presence of unusually high or low values. The median is more robust to outliers compared to the mean, making it a preferable choice for summarizing data if the dataset contains extreme values that might skew the average.

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