Basketball Stats: Range & Dispersion For Luis & Pedro

Oct 11, 2025 by ADMIN 54 views

Hey guys! Let's dive into some basketball stats and figure out the range and dispersion for two players, Luis and Pedro. We've got their scores from the last few games, and we're going to break it down. This is super useful for understanding how consistent each player is. So, let’s jump right in and get those numbers crunched!

Understanding Range and Dispersion in Basketball

Before we get into the nitty-gritty calculations, let's make sure we're all on the same page about what range and dispersion actually mean in the context of basketball stats. Range, in simple terms, is the difference between the highest and lowest scores. It gives us a quick snapshot of how much a player's performance fluctuates. A larger range means more variability, while a smaller range suggests more consistency. Think of it like this: if a player's scores are all over the place, their range will be big, but if they consistently score around the same number, their range will be small.

Measures of dispersion, on the other hand, give us a more detailed picture of how spread out the data is. The most common measures of dispersion are variance and standard deviation. Variance tells us the average of the squared differences from the mean, which sounds complicated, but it just means we're looking at how much each score deviates from the average score. We square the differences to get rid of negative signs and emphasize larger deviations. Standard deviation is then the square root of the variance, which gives us a more interpretable number in the same units as the original data (in this case, points). A higher standard deviation means the scores are more spread out, while a lower standard deviation means they're clustered closer to the average. Basically, these measures help us understand not just the high and low points, but the overall consistency of a player's scoring.

Why is this important? Well, coaches and analysts use these stats to evaluate players. A player with a high average but also high dispersion might be a bit of a gamble – they can have amazing games, but also really poor ones. A player with a lower average but low dispersion might be more reliable and consistent, even if they don't have those explosive scoring nights. Understanding these measures helps us paint a more complete picture of a player's performance beyond just their average score. So, with that in mind, let's get into the actual scores and see what we can learn about Luis and Pedro!

Luis's Range and Measures of Dispersion

Okay, let's start with Luis. We have his scores from the last few games: 18, 20, 20, 22, 20, 20. First up, we'll calculate the range, which is the easiest to find. To do this, we simply subtract the lowest score from the highest score. Looking at Luis's scores, the highest is 22 and the lowest is 18. So, the range is 22 - 18 = 4.

That's a pretty small range, guys! It suggests Luis has been fairly consistent in his scoring over these games. But let's dig a little deeper and find the measures of dispersion to get a more complete picture. We need to calculate the variance and standard deviation.

First, we need to find the mean (average) of Luis's scores. We add up all the scores and divide by the number of scores: (18 + 20 + 20 + 22 + 20 + 20) / 6 = 120 / 6 = 20. So, Luis's average score is 20 points.

Now, let's calculate the variance. This involves finding the difference between each score and the mean, squaring those differences, adding them up, and then dividing by the number of scores. Here we go:

(18 - 20)^2 = (-2)^2 = 4
(20 - 20)^2 = 0^2 = 0
(20 - 20)^2 = 0^2 = 0
(22 - 20)^2 = 2^2 = 4
(20 - 20)^2 = 0^2 = 0
(20 - 20)^2 = 0^2 = 0

Now we add these squared differences: 4 + 0 + 0 + 4 + 0 + 0 = 8. Then we divide by the number of scores: 8 / 6 = 1.33 (approximately). So, the variance of Luis's scores is about 1.33.

Finally, we calculate the standard deviation by taking the square root of the variance: √1.33 ≈ 1.15. So, the standard deviation is approximately 1.15 points.

What does this tell us? Well, the small standard deviation (1.15) confirms what the small range (4) suggested: Luis is a pretty consistent scorer. His scores tend to cluster closely around his average of 20 points. This consistency can be a valuable asset to a team!

Pedro's Range and Measures of Dispersion

Alright, let's shift our focus to Pedro and see how his stats stack up. Pedro's scores from the recent games are: 15, 17, 25, 24, 18, 21. Just like we did with Luis, we'll start by figuring out the range.

To find the range, we subtract the lowest score from the highest score. For Pedro, the highest score is 25 and the lowest is 15. So, the range is 25 - 15 = 10.

Notice that Pedro's range of 10 is more than double Luis's range of 4. This already hints that Pedro's performance might be more variable than Luis's. But let's confirm that with the measures of dispersion: variance and standard deviation.

First, we need to calculate Pedro's mean score. We add up all his scores and divide by the number of scores: (15 + 17 + 25 + 24 + 18 + 21) / 6 = 120 / 6 = 20. Interestingly, Pedro also has an average score of 20 points, the same as Luis!

Now, let's tackle the variance. We'll find the difference between each of Pedro's scores and his mean, square those differences, add them up, and divide by the number of scores:

(15 - 20)^2 = (-5)^2 = 25
(17 - 20)^2 = (-3)^2 = 9
(25 - 20)^2 = 5^2 = 25
(24 - 20)^2 = 4^2 = 16
(18 - 20)^2 = (-2)^2 = 4
(21 - 20)^2 = 1^2 = 1

Adding these squared differences gives us: 25 + 9 + 25 + 16 + 4 + 1 = 80. Now we divide by the number of scores: 80 / 6 = 13.33 (approximately). So, the variance of Pedro's scores is about 13.33.

Finally, we calculate the standard deviation by taking the square root of the variance: √13.33 ≈ 3.65. So, Pedro's standard deviation is approximately 3.65 points.

Pedro's standard deviation (3.65) is significantly higher than Luis's (1.15). This confirms our initial impression from the range: Pedro's scores are more spread out around his average. He has more games where he scores significantly higher or lower than his average, indicating less consistency than Luis.

Comparing Luis and Pedro: Consistency vs. Variability

Okay, guys, we've crunched the numbers for both Luis and Pedro. Let's put it all together and see what we've learned. We calculated the range, variance, and standard deviation for both players, and now we can directly compare their performance.

First off, both Luis and Pedro have the same average score: 20 points. This might lead you to think they are equally good scorers. However, the measures of dispersion tell a more nuanced story. This is why just looking at averages can be misleading!

Luis has a range of 4 points and a standard deviation of approximately 1.15 points. These relatively low numbers indicate that Luis is a very consistent scorer. His scores tend to cluster closely around his average of 20 points. He doesn't have huge swings in his performance from game to game.

Pedro, on the other hand, has a range of 10 points and a standard deviation of approximately 3.65 points. These higher numbers show that Pedro's performance is more variable. While he also averages 20 points, his scores fluctuate more. He has games where he scores significantly higher or lower than his average.

So, what does this mean in practical terms? Well, Luis is likely a more reliable scorer. You can generally count on him to score around 20 points each game. Pedro is more of a boom-or-bust player. He has the potential to have a huge scoring night, but he also has games where he might struggle. A coach might use these players differently based on their strengths and weaknesses. Luis might be the player you rely on for consistent scoring, while Pedro might be the player you look to for a spark or a big offensive game.

In conclusion, while averages give us a basic understanding of performance, measures of dispersion like range and standard deviation provide a much richer picture. They help us understand the consistency and variability of a player's performance, which is crucial for making informed decisions in basketball and many other areas!