Question

Suppose that you are tasked to measure a person's reaction time. You have them click on and off a

stop watch, and record the following times: 0.11, 0.26, and 0.36 seconds.
What is the standard deviation of these measurements?

Answer 1

The standard deviation of the given measurements is approximately 0.1027 seconds.

Explanation:

Find the mean (average) of the measurements by summing them up and dividing by the number of measurements:

⇒ Mean = (0.11 + 0.26 + 0.36) / 3 = 0.2433 seconds (rounded to four decimal places).

Calculate the differences between each measurement and the mean:

⇒ Difference1 = 0.11 - 0.2433 = -0.1333 seconds

⇒ Difference2 = 0.26 - 0.2433 = 0.0167 seconds

⇒ Difference3 = 0.36 - 0.2433 = 0.1167 seconds

Square each difference:

⇒ Squared Difference1 = (-0.1333)^2 = 0.01777789 seconds^2

⇒ Squared Difference2 = (0.0167)^2 = 0.00027889 seconds^2

⇒ Squared Difference3 = (0.1167)^2 = 0.01359389 seconds^2

Find the average of the squared differences (variance) by summing them up and dividing by the number of measurements:

Variance = (0.01777789 + 0.00027889 + 0.01359389) / 3 = 0.01055089 seconds^2 (rounded to eight decimal places).

Take the square root of the variance to obtain the standard deviation:

Standard Deviation = √0.01055089 seconds^2 ≈ 0.1027 seconds (rounded to four decimal places).