Reaction Time In an experiment conducted online at the...

Reaction Time In an experiment conducted online at the University of Mississippi, study participants are asked to react to a stimulus. In one experiment, the participant must press a key upon seeing a blue screen. The time (in seconds) to press the key is measured. The same person is then asked to press a key upon seeing a red screen, again with the time to react measured. The table shows the results for six study participants. (FIGURE CAN'T COPY) (a) Determine the mean, median, and mode reaction time for both blue and red. (b) Does there appear to be a difference in the reaction time? What might account for any difference? How might this information be used? (c) Suppose the reaction time of 0.841 for blue was incorrectly recorded as $8.41 .$ How does this affect the mean? the median? What property of the median does this illustrate?

Reaction Time In an experiment conducted online at the University of Mississippi, study participants are asked to react to a stimulus. In one experiment, the participant must press a key upon seeing a blue screen. The time (in seconds) to press the key is measured. The same person is then asked to press a key upon seeing a red screen, again with the time to react measured. The table shows the results for six study participants. (FIGURE CAN'T COPY)
(a) Determine the mean, median, and mode reaction time for both blue and red.
(b) Does there appear to be a difference in the reaction time? What might account for any difference? How might this information be used?
(c) Suppose the reaction time of 0.841 for blue was incorrectly recorded as $8.41 .$ How does this affect the mean? the median? What property of the median does this illustrate?

Key Concepts

Arithmetic Mean

The arithmetic mean is a measure of central tendency calculated by summing all the values and then dividing by the number of values. It provides a simple summary of the data but can be easily influenced by very high or very low values, known as outliers, which can skew the result and give a misleading sense of the typical value.

Median

The median is the middle value in a data set when the values are arranged in numerical order. It is a robust measure of central tendency because it is less sensitive to outliers or extreme scores. This characteristic makes the median particularly useful when the data distribution is skewed or contains errors.

Mode

The mode is the value that appears most frequently in a data set. It is a useful measure of central tendency, especially for categorical data or for data sets where some values occur much more frequently than others, but it may not provide a complete picture when the data have a uniform distribution or multiple modes.

Outliers and Robustness of Statistical Measures

Outliers are values that are significantly different from the rest of the data. Their presence can greatly affect certain statistical measures, such as the mean, causing it to shift and potentially misrepresent the central tendency. In contrast, the median is robust to outliers, meaning that extreme values have little impact on its value. This robustness makes the median a valuable statistic when the data may contain errors or anomalous values.

Transcript

00:01 Alrighty.

00:03 So for number 20 here in this 3 .1 lesson, this is talking about reaction times, two colors.

00:11 So like, what was the person's reaction time in seconds? asked to press a key whether they're seeing a red, when they see red, or when they see blue.

00:22 And so they're asking us in part a to determine the mean median mode reaction time for both blue and red.

00:30 We're going to start with blue.

00:33 So what you're going to do for the blue is you're going to have your mean of adding up the 0 .582 plus 0 .481 plus 0 .841 plus 0 .267 plus 0 .685 and plus 0 .45.

00:54 And that's going to add up to 3 .306 and then you divide that by the total number and that's six so that's going to be 0 .551 seconds.

01:12 Now the median can be found by locating the third and fourth number in the list from smallest to largest.

01:23 So if you look at that short list and you kind of order them out from shortest to largest, you're going to end up with 0 .481 and 0 .582, and you're going to add those up and divide by 2 to get 0 .531 seconds.

01:49 Now, there is no mode because there are no repeats.

01:54 You would just say mode none.

01:58 To continue with part a, we have to find the mean of the red lights, and those reaction times.

02:08 So the mean there would be adding up all six numbers and dividing by six.

02:15 So when i add 0 .408 all the way down to the 0 .533, i add up all those six numbers.

02:21 You should get 2 .748, divide that by 6.

02:27 You're going to get 0 .458 seconds.

02:33 Then the median can be found similarly as we did before, where you locate the third and the fourth number in that list, which ends up being 0 .408 plus 0 .456.

02:51 Remember, these have to be in order from smallest to largest, and it's the number that's going to be between the third and the fourth entry because there's six entries, so that's halfway through.

03:00 You're going to add the 0 .408 and 0 .456, and divide that by 2...

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