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AP STATS Unit 1
AP Statistics
| Term | Definition |
|---|---|
| Categorical variable | Takes on values that are category names or group labels |
| Quantitative variable | Takes on numerical values for a measured or counted quantity |
| Individuals | People, animals, or things described by a set of data |
| Variable | Characteristics that changes from one individual to another |
| Frequency table | Gives the number of individuals(cases) in each category |
| Relative Frequency table | Gives the proportion or percent of individuals (cases) in each category |
| Tabular representation of data | The given data set is presented in rows and columns |
| Counts and relative frequencies (percentages or proportions) | Reveal information that can be used to justify claims about the data in context. |
| Label Axes | Variable name on horizontal axis; Frequency/ Relative frequency on vertical axis |
| Scale Axes | Categorical labels spread out along horizontal axis; Start scaling vertical axis at 0 and go up in equal increments until equal or exceed maximum frequency/relative frequency. |
| Draw Bars | Make bars equal in width and leave gaps between them The heights of the bars represent the category frequencies or relative frequencies. |
| Key or legend | Connects categories to graph/pie pieces |
| Bar chart | Displays categorical frequencies or relative frequencies, same as a pie chart |
| Graphical representations | Categorical variables reveal information that can be used to justify claims about the data in context. |
| Discrete variable | Can take on a countable number of values (with gaps)- counting |
| Continuous variable | Can take on infinitely many values, but those values cannot be counted (no gaps)- measuring |
| Distribution | Describes the values the variables takes and the frequency it takes these values |
| Dot plot | Visually groups the number of data points in a data set based on the value of each point |
| Stem and leaf plot | Used to organize data as they are collected. Each day is split into a "stem" (the leading digit or digits) and "leaf"(the trailing data) |
| Histogram | A graphical display of data using bars of different heights (quantitative data) |
| SOCS | S: Shape-symmetric, skewed, approximately normal, modes(peak) unimodal, bimodal, trimodal, multimodal, uniform O: Outlier-points that don't follow the pattern of the rest of the data. C: Center-mean or median S: Spread-range of the data |
| Mean | Sum of all the data values divided by the number of values |
| Median | Middle value of an ordered data set (odd number of values) |
| Q1 | The first quartile, Q1, is the median of the first half of the ordered data set |
| Q3 | The third quartile, Q2, is the median of the second half of the ordered data set |
| IQR | Interquartile Range, IQR, is the amount of spread in the middle of a data set. IQR=Q3-Q1 |
| Range | The difference between the maximum value and the minimum data value |
| Standard Deviation | Typical distance that each value is away from the mean |
| Variance | The square of standard deviation |
| Outliers | Data points that are significantly different from the rest of the data in a data set. Upper boundary: Q3+ 1.5IQR. Lower Boundary Q1+1.5IQR. A value located 2 or more standard deviations above, or below, the mean. |
| 5# summary (include outlier) | Min, Q1, Median, Q3, Max |
| The mean, SD, and range | Non resistant |
| Median and the IQR | Resistant |
| Association | There is an association between 2 variables if knowing the outcome of one variable affects the outcome of the other variable. |
| Skewed right distribution | mean>median |
| Skewed left distribution | mean<median |
| Symmetric distribution | mean=median |
| Segmented bar graph is the same | No association |
| Segmented bar graph is not the smae | Yes association |
| Marginal Relative Frequency | The ration between the frequency of a row total or column total to the total frequency of the data (B/C ) |
| Joint Relative Frequency | The ratio of the frequency in a particular category and the total number of data values (A/C) |
| Conditional Relative Frequency | A statistical concept that helps interpret data by focusing on specific subsets of a population rather than the entire data sets (A/B) |
| Calculator for plots? | Enter data: STAT → EDIT. For plots: 2nd → Y= → turn Plot 1 on. Choose boxplot, histogram, or scatter. Zoom nicely: ZOOM → 9 (ZoomStat). |
| How do histograms work? | Break data into bins of equal width (same size “containers”). The height of each bar = how many data points in that bin. Describe: center, spread, skewness, shape. |
| How do you describe outliers? | Use the 1.5×IQR Rule: Calculate IQR = Q3 – Q1. Outlier if: below Q1 – 1.5×IQR above Q3 + 1.5×IQR |
| What’s the five-number summary telling us? | Minimum, Q1, Median, Q3, Maximum. Between each point is 25% of the data. Min→Q1 = 25% Q1→Median = 25% Median→Q3 = 25% Q3→Max = 25% |
| How do you describe a boxplot? | Based on five-number summary: min, Q1, median, Q3, max. Boxes show the middle 50% (the “meat of the sandwich”), whiskers stretch to min/max (unless there are outliers). Outliers = dots/stars outside 1.5×IQR. |
| What’s a stem plot and how do you read it? | Split numbers into stem (tens place, like a tree trunk) and leaf (ones place, little branches). Order matters—smallest to biggest. Helps see shape and clusters quickly. |
| How do you label a graph in AP Stats? | Imagine SOCS as four socks on a clothesline—each one stretched differently (spread), sagging in the middle (center), one sock hanging way too far down (outlier), and the overall line leaning left or right (skew). |
Created by:
Leo12345
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