--- title: "Statistic — AP Statistics Definition & Exam Guide" description: "A statistic is a number that summarizes sample data, like x̄ or s. Learn how it differs from a parameter and why sampling variability makes it central to Unit 5." canonical: "https://fiveable.me/ap-stats/key-terms/statistic" type: "key-term" subject: "AP Statistics" --- # Statistic — AP Statistics Definition & Exam Guide ## Definition In AP Statistics, a statistic is a numerical summary calculated from sample data, such as the sample mean (x̄), sample standard deviation (s), or sample proportion (p̂). Statistics vary from sample to sample and are used to estimate population parameters. ## What It Is A statistic is any number you calculate from a **[sample](/ap-stats/unit-1/random-sampling-data-collection/study-guide/nQz8XwRMmIKKBS59qrew "fv-autolink")**. The [sample mean](/ap-stats/key-terms/sample-mean "fv-autolink") x̄, the sample standard deviation s, the median, the IQR, a sample proportion p̂: all of these are statistics because they come from data you actually collected, not from the entire population. Here's the idea that powers the whole course: statistics **vary**. If you take a sample of 50 students and compute the mean height, then take a different sample of 50 students, you'll get a different x̄. Neither sample is wrong. That sample-to-sample [variation](/ap-stats/unit-5 "fv-autolink") is random, and it's exactly what Topic 5.1 asks you to think about. The CED puts it plainly in 1.7.A, "a statistic is a numerical summary of sample data," and in 5.1.A, where you identify questions raised by variation in statistics from samples taken from the same population. Later units build entire inference procedures around how much a statistic typically wiggles. ## Why It Matters The term lives in two places in the CED. In **[Unit 1](/ap-stats/unit-1 "fv-autolink") (Topic 1.7)**, learning objectives 1.7.A, 1.7.B, and 1.7.C have you calculating and choosing statistics: [measures of center](/ap-stats/key-terms/measures-of-center "fv-autolink") (mean, median), measures of variability (range, IQR, standard deviation), and deciding which ones to use when outliers are present. The mean and standard deviation are nonresistant (outliers drag them around), while the median and IQR are resistant. In **Unit 5 (Topic 5.1)**, the focus flips from computing a statistic to asking why your statistic doesn't match your friend's. That question, "why is my sample not like yours?", is the doorway to sampling distributions, and sampling distributions are the engine behind every confidence interval and significance test in Units 6-9. If you don't get the statistic vs. parameter distinction down cold, the second half of the course gets confusing fast. ## Connections ### [Parameter (Units 1 & 5)](/ap-stats/key-terms/parameter) A [parameter](/ap-stats/key-terms/parameter "fv-autolink") is the same kind of number as a statistic, but for the whole population instead of a sample. The mean is x̄ when it's a statistic and μ when it's a parameter. The entire point of inference is using the statistic you have to estimate the parameter you don't. ### Mean and Median (Unit 1) These are the two big measures of center, and choosing between them is a 1.7.C skill. The mean is nonresistant (an outlier yanks it toward the tail), while the [median](/ap-stats/key-terms/median "fv-autolink") is resistant. When mean > median, suspect right skew. ### [Interquartile Range (IQR) (Unit 1)](/ap-stats/key-terms/interquartile-range-iqr) The IQR is the resistant measure of [spread](/ap-stats/key-terms/spread "fv-autolink"), and it powers the 1.5 × IQR outlier rule. Pair the median with the IQR for skewed data, and the mean with the standard deviation for roughly symmetric data. ### Inferential Statistics (Units 5-9) Once you know a statistic varies randomly from sample to sample, you can model that variation with a sampling distribution. That model is what lets you say how confident you are that a statistic is close to the true parameter. ## On the AP Exam Multiple-choice questions love handing you a set of summary statistics and asking what they reveal. You might get a five-number summary (Min = 12, Q1 = 15, Median = 22, Q3 = 35, Max = 89) and have to spot right skew, or a mean of 75 vs. a median of 72 and infer the distribution's shape. Other stems ask which statistics detect outliers (median and IQR with the 1.5 × IQR rule) or how a linear transformation changes the mean, median, and standard deviation. On FRQs, you're expected to use correct notation (x̄ and s for a sample, μ and σ for a population) and to justify your choice of statistic. The 2017 exam's free-response set leaned on summary statistics throughout, from comparing distributions of melon diameters to evaluating evidence from a sample of 207 patients. Sloppy notation, like writing μ for a sample mean, costs you on the rubric, so label every number as a statistic or a parameter. ## Statistic vs Parameter A statistic describes a sample; a parameter describes a population. Easy mnemonic: Statistic and Sample both start with S, Parameter and Population both start with P. Notation matters too. The sample mean is x̄ and the sample standard deviation is s (statistics), while the population mean is μ and the population standard deviation is σ (parameters). Statistics change from sample to sample; a parameter is a fixed (usually unknown) number. You calculate statistics to estimate parameters. ## Key Takeaways - A statistic is a numerical summary calculated from sample data, like x̄, s, the median, the IQR, or p̂. - Statistics estimate parameters: x̄ estimates μ, s estimates σ, and p̂ estimates p, so notation tells the grader you know which is which. - Statistics vary from sample to sample, and that random variation is the central question of Topic 5.1 and the foundation of all inference. - The mean, standard deviation, and range are nonresistant statistics because outliers pull on them, while the median and IQR are resistant. - When choosing summary statistics, use median and IQR for skewed distributions or data with outliers, and mean and standard deviation for roughly symmetric distributions. ## FAQs ### What is a statistic in AP Statistics? A statistic is a number calculated from sample data that summarizes some feature of the sample, like the sample mean x̄, sample standard deviation s, or sample proportion p̂. It's the sample-based counterpart to a population parameter. ### What's the difference between a statistic and a parameter? A statistic comes from a sample and varies between samples; a parameter describes the whole population and is fixed but usually unknown. Remember: Statistic-Sample, Parameter-Population. x̄ and s are statistics, μ and σ are parameters. ### Is the median a statistic? Yes, if it's computed from a sample. Any numerical summary of sample data is a statistic, including the median, IQR, range, quartiles, and mean. The same quantity computed for an entire population would be a parameter. ### Why do two samples from the same population give different statistics? Because of random sampling variability. Each random sample contains different individuals, so summaries like x̄ shift from sample to sample. Topic 5.1 (LO 5.1.A) asks you to recognize this variation and decide whether it looks random or suspicious. ### Which statistics should I use when a distribution has outliers? Use the median and IQR, because they're resistant (outliers barely move them). The mean, standard deviation, and range are nonresistant, so a single extreme value can distort them. 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