So, what is standard deviation. The standard deviation is a measurement of dispersion around the mean or average. The best way to explain this
is through an example. Let’s say that you are looking to purchase some wireless earbuds. You have done your research, and are down to a choice of two models,
A and B. One of the most important aspects of the earbuds is their hours of playtime per charge. Both models, A and B, have listed an average playtime of 36 hours
per charge. You snoop around online and find a chart for the average playtime for each pair. The chart shows that, for each model, 6 different pairs of each model
were tested. Here is the chart for model A, the first pair lasted 31 hours, the 2nd pair lasted 32 hours and so on. To calculate the average, we sum these up,
to get 216 hours. Next, we divide by the number of pairs, which is 6, and get 36 hours as the average, which is what the manufacture claimed.
Next, we look at the chart for model B, which is listed here. Now we go through the same process to find the average, sum them up to get 216, then divide by the number
of pairs, which is 6, and get 36 hours as the average, which again, is what the manufacture claimed. So, now we might think that this is a draw, both pairs of
earbuds have the same average playtime. But, if we calculate the standard deviation, it will show that this is not true. Let’s start with model A.
We calculate the standard deviation by first creating a column and we going to title it earbud x minus the average. For each pair of earbuds, we are going to take the
playtime hours result and subtract the average from it. For pair 1 we have a playtime of 31 hours, so we subtract the average for model A from it, 31 hours minus 36 hours
equals, -5 hours. One note here. If we draw a number line and place the average of 36 hours in the middle of it, and draw a line for 31 over here, the value of pair 1 for model
A, this distance of negative 5 hours is deviation from the mean. And next, we do the same for pair 2, 32 minus 36 equals -4 hours, and we continue this for the 4 remaining
pairs. Now, if we total this column up we get zero. Which is what we want, getting a sum total of zero from this column means that the average we calculated is accurate.
The next step in calculating the standard deviation is to take the values in column 3, the column we just created and square each of those values.
So, we are going to create a 4th column and title it, earbud x minus the average, quantity squared. So for pair 1 we had -5 in column 3, so, we will square -5,
-5 times -5 is positive 25. Next, we do the same for pair 2, which was negative 4, -4 times -4 is positive 16. And we will continue this process for the other 4 pairs
of model A. Now that column 4 is complete, we will sum that up, or add up that column, which results in 106 hours squared. The next step in calculating the standard
deviation is to take the result from column 4, and divide it by the number of data points, or in this case the number of pairs of earbuds of model A, which is 6.
So, 106 hours squared divided by 6, and this results in 17.667 hours squared rounded off. And this value of 17.667 is called the variance.
The problem with this value is that it is in hours squared. Well, we can remedy that by taking the square root of that value to get it to just regular hours.
So, the square root of 17.667 hours squared equals 4.20 hours, rounded off. And this value of 4.20 hours is the standard deviation. And The standard deviation, by itself
doesn’t really tell us much, as we need something to compare it to. So, on the screen is the process for going through and getting the standard deviation
for the model B earbuds. And this results in a standard deviation of 5.45 hours rounded off. Now, we can compare the standard deviations of each of the models.
For model A we have 4.20 hours and for model B we have 5.45 hours. So, model A has a standard deviation of 1.25 hours less than model B.
What this means is that model A’s data points, as a whole, are much closer to it’s average than model B’s. So, there is less variation for the average playtime
in the earbuds of model A. And here is a dot plot, which is a type of graph, that shows this concept visually. As you can see, for the exact same number line,
the points on the plot are not as scattered out for model A. So, based on the standard deviation, model A would be the better, more consistent pair of earbuds to purchase.
Alright my friends, hopefully you got something out of this video, I do have more videos right there for you, till next time, I am outta here.