Understanding Variance in Data
Saurabh Vanikar
|| Senior IT Manager at Allern Enterprises || IT professional with 15+ years of experience in IT infrastructure, service management, cloud services (AWS/Azure), data security || SQL || Python|| Data Analysis Enthusiast||
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Imagine we're at a pizza restaurant and we order a Margherita pizza. Let's say we've had this pizza many times before from different restaurants or even the same restaurant on different days. Each time we order it, the pizza might taste slightly different.
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Variance is like measuring how much these tastes differ from each other. If the taste is pretty consistent every time we order it, the variance is low. But if sometimes it's super cheesy, and other times it's barely cheesy, then the variance is high.
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So, in simpler terms, variance measures how spread out or varied the different experiences of the same thing (in this case, the taste of the pizza) are. Low variance means things are pretty consistent, while high variance means there's a lot of difference between each experience.
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When we look at variance, we can make a few inferences:
Consistency: Low variance suggests that things are pretty consistent or stable. For example, if we order the same pizza from the same restaurant, and it tastes almost the same each time, then the variance is low. This consistency can be reassuring because we know what to expect.
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Variability: High variance tells us that things are quite different from each other. So, if we order the same pizza from different places and each time it tastes very different, then the variance is high. This variability can make it more unpredictable or exciting but might also mean we're not always getting what we expect.
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Reliability: Variance can also tell us about how reliable or dependable something is. Low variance suggests reliability because we can rely on things being similar each time. High variance might mean less reliability because there's more uncertainty about what we'll get.
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So, in simpler terms, variance helps us understand how consistent or varied something is, which can influence our expectations and decisions.
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Population variance and sample variance are both ways to measure how spread out or varied a set of data points is, but they're calculated differently depending on whether we're looking at the entire population or just a sample of it.
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1. Population Variance: This is used when we have data for an entire population, meaning we have information about every single member of the group we're interested in. To calculate population variance, we take the average of the squared differences between each data point and the mean of the population.
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?? Population Variance = Σ((x - μ)2) / N
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?? Where:
?? - Σ represents the sum of all the terms,
?? - x is each individual data point,
?? - μ is the mean (average) of the entire population,
?? - N is the total number of data points in the population.
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2. Sample Variance: This is used when we only have data for a subset, or sample, of the population. Sample variance is similar to population variance, but it uses a slightly different formula to account for the fact that we're dealing with a smaller subset of the population.
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?? Sample Variance = Σ((x - x?)2) / (n - 1)
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?? Where:
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?? - Σ represents the sum of all the terms,
?? - x is each individual data point,
?? - x? is the mean (average) of the sample,
?? - n is the number of data points in the sample.
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The key difference between population and sample variance lies in the denominator. In population variance, we divide by the total number of data points (N), while in sample variance, we divide by the sample size minus one (n - 1). This adjustment in the sample variance formula helps to provide a more accurate estimate of the variability in the population based on the sample data.
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Let’s imagine we’re trying to determine how consistently a pizza restaurant makes Margherita pizzas. We have two scenarios:
?1. Population Variance: We have data on every Margherita pizza the restaurant has ever made. This means we know exactly how each pizza tasted because we've tried every single one they've ever made. To calculate the population variance, we'd measure the difference between the taste of each pizza and the average taste of all pizzas made by that restaurant. This would give us an idea of how much the taste varies across all pizzas they make.
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2. Sample Variance: Instead of trying every single pizza, we decide to try a smaller number of pizzas, maybe just ten of them. Now, we're not trying every pizza the restaurant makes, but we're using this smaller sample to estimate the overall consistency of their pizzas. To calculate the sample variance, we'd measure the difference between the taste of each pizza in our sample and the average taste of those ten pizzas. This would give us an estimate of how much the taste varies among the pizzas we tried.
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In both cases, we're trying to understand how consistent or varied the taste of the Margherita pizzas is, but the way we calculate the variance depends on whether we have data on every single pizza (population variance) or just a smaller subset of them (sample variance).
Thank you
Saurabh Vanikar
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Please find the links to my previous posts.
Post 1 — Statistics is Everywhere
Post 2 — Types of Statistics
Post 3 — Central Tendency of the Distribution
Post 4 — What is Data?
Post 5 — Types of data
Post 6 — Sampling Techniques Part 1
Post 7 — Sampling Techniques Part 2
Post 8 — Sampling Techniques Part 3
Post 9 — Hypothesis Testing
Post 10 — Variables
Post 12?—?Measures of Dispersion & Range
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