Standard Deviation 04:34 minutes

Video Transcript

Transcript Standard Deviation

Cliff is a businessman and plans to set up his own basketball team. He loves numbers and is a really careful planner, so he hates it when things don't go as expected. Instead of a few really good players and an equal number of poor players, Cliff decides to choose players who are all consistently good. To achieve his goal of winning a championship, Cliff needs to use Standard Deviation to evaluate players' performances before he chooses his team. Cliff got the lowdown on several players from a reliable source he met in a sports bar. Cliff's contact gave him the box scores for the last 5 games for each of the players Cliff is evaluating.

The Standard Deviation

Let’s see how to calculate the Standard Deviation of the box scores of each player. The sign for Standard Deviation is called sigma, which is a lowercase Greek letter and looks like this. And the formula to calculate the Standard Deviation is: the square root of the average of the squares of the difference between each element in the set and the mean of the set.

Calculating the Standard Deviation

Now we can calculate the Standard Deviation of the scoring for the first player, Martin McTry. His scores look like this. Since there are 5 games' worth of scoring data, 'n' equals 5. Remember, you can find the mean of the set by summing all the elements of the set and dividing by the total number of elements in the set. We sum the player's scoring totals for each of the 5 games and finally divide by 5 to see that Martin McTry averaged 20 points in his last 5 games.

Now that we have the mean, we can use this to find Martin McTry's scoring standard deviation. We can just plug in n=5, as well as the mean of the set, 20, and subtract each of the point totals for each of the five games for 'x' sub 1 to 'x' sub 5. Apply some PEMDAS -- Parentheses first, then exponents, as well as addition and for our final step, we take the square root of 38 over 5 giving us approximately 2.757.

The last 5 games for the second player Cliff is scouting, Lance Layton, looked like this: Layton also played in 5 games, so 'n' equals five again. We need his scoring average next, so we total his scoring from the last 5 games and divide by n = 5, which gives us the averageand we find out that Lance Layton also averaged 20 points per game over the last 5 games. Let's look and see if Lance Leyton's standard deviation is as low as Martin McTry's. We just plug n=5 into the standard deviation formula as well as the mean, 20, and the per game scoring for 'x' sub 1 to 'x' sub 5 apply some PEMDAS again and finally, take the square root of 336 over 5 giving us approximately 8.198.

Comparing Martin McTry's and Lance Layton's recent scoring outputs, the average for both players over the past 5 games is 20 points per game. But with a standard deviation of 2.757, Martin McTry is a far more consistent player compared to Lance Layton with a standard deviation of 8.198.

After calculating the Standard Deviation for each player, Cliff is able to set up his team the way he wants. Cliff's excited to begin the path to the championship! Some reliable source - those might as well be their bingo scores!!!

  1. Eugene

    Great! I'm glad the video was helpful! We'll continue to work hard to provide you with fun, accessible explanations.

    Posted by Eugene L., 6 months ago
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    This is helpful for understanding standard deviation! Thank you so much!

    Posted by Plano Kellmeyer, 6 months ago