Question

actual times (in seconds) recorded when statistics students participated in an experiment to test their ability to determine when one minute (60 seconds) had passed are shown below. find the mean, median, and mode of the listed numbers. 55 52 73 64 67 60 47 47 the mean is □ sec. (round to the nearest tenth as needed.) the median is □ sec. (round to the nearest tenth as needed.) what is(are) the mode(s)? select the correct choice below and, if necessary, fill in the answer box within your choice. a. the mode(s) is(are) □ sec. (use a comma to separate answers as needed.) b. there is no mode.

Explanation:

Step1: Calculate the mean

First, find the sum of the data values: $55 + 52+73 + 64+67+60+47+47 = 465$. There are $n = 8$ data - points. The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{465}{8}=58.125\approx58.1$ seconds.

Step2: Calculate the median

Arrange the data in ascending order: $47,47,52,55,60,64,67,73$. Since $n = 8$ (an even number), the median is the average of the two middle values. The two middle values are the $4^{th}$ and $5^{th}$ ordered values. Median $=\frac{55 + 60}{2}=\frac{115}{2}=57.5$ seconds.

Step3: Calculate the mode

The mode is the value that appears most frequently in the data - set. The number $47$ appears twice, and all other numbers appear only once. So the mode is $47$ seconds.

Answer:

The mean is $58.1$ sec.
The median is $57.5$ sec.
A. The mode(s) is(are) $47$ sec.