Question

The data below are times (in seconds) recorded when statistics students participated in an experiment to test their ability to determine when 1 minute (60 seconds) had passed. Find the mean, median, and mode. What do these data suggest about students perception of time?

55 51 74 61 67 60 49 49

What is the mean? Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. The mean is ___ sec (round to the nearest tenth as needed.)

B. There is no mean.

Answer 1

Mean = 58.25

Median = 57.5

Mode = 49

Explanation:

We are given the following data set:

55, 51, 74, 61, 67, 60, 49, 49

Formula:

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`Mean =\displaystyle(466)/(8) = 58.25`

Sorted data:

49, 49, 51, 55, 60, 61, 67, 74

Mode is the entry with highest frequency.

49 appeared two times.

Mode = 49

Formula:

`Median:\\\text{If n is odd, then}\\\\Median = \displaystyle(n+1)/(2)th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle((n)/(2)th~term + ((n)/(2)+1)th~term)/(2)`

`\text{Median} = (55+60)/(2) = 57.5`

All these are less than 60 seconds, which indicates that students perceive 1 minute to pass sooner than it actually has.