Standard Deviation, Mean, Median & Mode

ERRATA: The Mean of (1+3+3+5+7+10+100) / 7 is 18.43, NOT 22 like I mentioned in the video. The text below has been corrected and a note has been added to the appropriate point in the video

Mean, Median and Mode Robustness Definition Calculate

Mean (average) = The sum of all of the values divided by the number of values. Least Robust
Median (“middle” value) = The value that is in the middle when all of the values are arranged in ascending order. If there is an even number of values there is no single middle value. Therefore, you take the average of the two middle value. Robustness is in between mean and mode
Mode (most common value)  = The value that appears the highest number of times. Most Robust

 

If you are given the list of values 1, 3, 3, 5, 7, 10. What is the mean, median, and mode?

  • Mean = (1+3+3+5+7+10) / 6 = 4.83
  • Median = average of the 2 middle values since there is an even number of values. (3+5)/ 2 = 4
  • Mode = most frequent value = 3

 

If you take the list of values from the previous question but now add an additional value of 100 how does the mean, median, and mode change?

  • Mean = (1+3+3+5+7+10+100) / 7 = 18.43
  • Median = middle value = 5
  • Mode = most frequent value = 3

 Robustness

The above question illustrates how Robust, or resistant to change by an extreme value, the three measures of central tendency are. You can see that by adding one extreme value (an outlier) the mean has changed a lot and mode hasn’t changed at all. This is because mean is the least robust of the three values and mode is the most robust. Median is less robust than mode, but more robust than mean.

On Step 1 you may also be asked to compare mean, median, and mode in certain situations based on a histogram or set of values. For example, the answer looks like “mean is greater than mode” rather than a precise numerical answer. In most of these cases the data is skewed significantly in one direction and is not normally distributed.

Normal Distribution, Normally Distributed, Skewed Right, Skewed Left, Positive Skew, Negative Skew, Negatively Skewed, Positively Skewed

 

 Standard Deviation

Standard deviation (greek symbol σ) measures how much the values in a data set differs from the mean. In other words, standard deviation measures dispersion or variability in a set of values. A data set with mostly similar values has a small standard deviation, while a data set with very different values has a large standard deviation.

Standard deviation changes with changes in sample size (number of values or participants). With small sample sizes random chance has a bigger impact and therefore standard deviation for a small sample size is generally larger. Studies with more values generally have smaller standard deviations as chance plays less of a role.

 

Now that you are done with this video you should check out the next video in the Biostats & Epidemiology for the USMLE Step 1 section which covers 2 by 2 Tables, False Positive, False Negative, True Positive & True Negative

 

 

8 thoughts on “Standard Deviation, Mean, Median & Mode”

      1. Yes you are absolutely correct. I must have typed it in wrong into my calculator. The right answer is 18.43. Sorry about that. I’ll add a note to the video and webpage soon. Thank you so much for pointing it out and I’m sorry about the slow response

  1. Standard deviation changes with changes in sample size (number of values or participants). With small sample sizes random chance has a bigger impact and therefore standard deviation for a small sample size is generally larger. Studies with more values generally have smaller standard deviations as chance plays less of a role.

    I dont think it is the case. I think Standard deviation remains the same, what varies is the standard error… is that it?.please help….this question has appeared in step 1

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