**Video Transcript**

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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!!!

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

This is helpful for understanding standard deviation! Thank you so much!