AP Statistics

Question 1

Individuals

Answer 1

Individuals are any data set that contains information about a group. The group that is being studied or experimented.

Question 2

Variable

Answer 2

A variable is an attribute that describes a person, place, thing, or idea.
The value of the variable can “vary” from one entity to another.
For example, suppose we let the variable x represent the color of a person’s hair. The variable x could have the value of “blond” for one person, and “brunette” for another.

Question 3

Categorical Variable

Answer 3

Categorical. Categorical variables take on values that are names or labels. The color of a ball (e.g., red, green, blue) or the breed of a dog (e.g., collie, shepherd, terrier) would be examples of categorical variables.

Question 4

Quantitative Variable

Answer 4

Quantitative. Quantitative variables are numerical. They represent a measurable quantity. For example, when we speak of the population of a city, we are talking about the number of people in the city - a measurable attribute of the city. Therefore, population would be a quantitative variable.

Question 5

Discrete Variables

Answer 5

Suppose we flip a coin and count the number of heads. The number of heads could be any integer value between 0 and plus infinity. However, it could not be any number between 0 and plus infinity. We could not, for example, get 2.5 heads. Therefore, the number of heads must be a discrete variable.

Question 6

Continuous

Answer 6

Suppose the fire department mandates that all fire fighters must weigh between 150 and 250 pounds. The weight of a fire fighter would be an example of a continuous variable; since a fire fighter’s weight could take on any value between 150 and 250 pounds.

Question 7

Univariate Data

Answer 7

Univariate data. When we conduct a study that looks at only one variable, we say that we are working with univariate data. Suppose, for example, that we conducted a survey to estimate the average weight of high school students. Since we are only working with one variable (weight), we would be working with univariate data.

Question 8

Bivariate Data

Answer 8

Bivariate data. When we conduct a study that examines the relationship between two variables, we are working with bivariate data. Suppose we conducted a study to see if there were a relationship between the height and weight of high school students. Since we are working with two variables (height and weight), we would be working with bivariate data

Question 9

Population

Answer 9

In statistics, population refers to the total set of observations that can be made.

For example, if we are studying the weight of adult women, the population is the set of weights of all the women in the world. If we are studying the grade point average (GPA) of students at Harvard, the population is the set of GPA’s of all the students at Harvard.

Question 10

Sample

Answer 10

In statistics, a sample refers to a set of observations drawn from a population.

Often, it is necessary to use samples for research, because it is impractical to study the whole population. For example, suppose we wanted to know the average height of 12-year-old American boys. We could not measure all of the 12-year-old boys in America, but we could measure a sample of boys.

Question 11

Census

Answer 11

A census is a study that obtains data from every member of a population. In most studies, a census is not practical, because of the cost and/or time required.

Question 12

Distribution

Answer 12

The distribution of a statistical data set (or a population) is a listing or function showing all the possible values (or intervals) of the data and how often they occur. When a distribution of categorical data is organized, you see the number or percentage of individuals in each group.

Question 13

Inference

Answer 13

The process of using data analysis to deduce properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates.

Question 14

Frequency Table

Answer 14

When a table shows frequency counts for a categorical variable, it is called a frequency table Below, the bar chart and the frequency table display the same data

Question 15

Relative Frequency

Answer 15

A frequency count is a measure of the number of times that an event occurs.

To compute relative frequency, one obtains a frequency count for the total population and a frequency count for a subgroup of the population. The relative frequency for the subgroup is:

Relative frequency = Subgroup count / Total count

The above equation expresses relative frequency as a proportion. It is also often expressed as a percentage. Thus, a relative frequency of 0.50 is equivalent to a percentage of 50%.

Question 16

Table

Answer 16

The values of the cumulative distribution functions, probability functions, or probability density functions of certain common distributions presented as reference tables for different values of their parameters.

Question 17

Pie Chart

Answer 17

A pie chart (or a circle chart) is a circular statistical graphic, which is divided into slices to illustrate numerical proportion. In a pie chart, the arc length of each slice (and consequently its central angle and area), is proportional to the quantity it represents.

Question 18

Bar Graph

Answer 18

A bar chart is a graphical representation of the categories as bars. … A bar chart can be plotted vertically or horizontally. Usually it is drawn vertically where x-axis represents the categories and y-axis represents the values for these categories.

Question 19

Two-way Table

Answer 19

A two-way table (also called a contingency table) is a useful tool for examining relationships between categorical variables. The entries in the cells of a two-way table can be frequency counts or relative frequencies (just like a one-way table ).

Question 20

Marginal Distribution

Answer 20

Entries in the “Total” row and “Total” column are called marginal frequencies or the marginal distribution. Entries in the body of the table are called joint frequencies.

Question 21

Conditional

Answer 21

Conditional probability is the probability of one event occurring with some relationship to one or more other events. For example: Event A is that it is raining outside, and it has a 0.3 (30%) chance of raining today. Event B is that you will need to go outside, and that has a probability of 0.5 (50%).
The formula for conditional probability is:

P(B|A) = P(A and B) / P(A)

which you can also rewrite as:

P(B|A) = P(A∩B) / P(A)

Question 22

Segmented Bar Graph

Answer 22

A segmented Bar chart is one kind of stacked bar chart, but each bar will show 100% of the discrete value. For example, there are a total of 40 students in your classroom. Out of them, 25 students like Basketball, 30 students like Volleyball, and 20 students like Badminton. There are 25 boys and 15 girls in the class. The data along the vertical side of the box represents sports while the horizontal represents a certain percentage for each sport. Each bar will show the preference of each sport according to the number of boys and girls and the bars will be separated by stacked order, representing one group for the boys and the other for the girls.

Question 23

Side by Side Bar

Answer 23

In a side-by side bar chart, the bars are split into colored bar segments. The bar segments are placed next to each other. … In a stacked bar chart, the bar segments within a category bar are placed on top of each other, and in a side-by-side bar chart, they are placed next to each other.

Question 24

Graph

Answer 24

A statistical graph or chart is defined as the pictorial representation of statistical data in graphical form. The statistical graphs are used to represent a set of data to make it easier to understand and interpret statistical data.

Question 25

Association

Answer 25

In Statistics, association tells you whether two variables are related. The direction of the association is always symbolized by a sign either positive (+) or negative (-).

Question 26

Simpson’s Paradox

Answer 26

Simpson’s paradox, which goes by several names, is a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined.

Question 27

Dot Plot

Answer 27

A Dot Plot, also called a dot chart or strip plot, is a type of simple histogram-like chart used in statistics for relatively small data sets where values fall into a number of discrete bins (categories).

Question 28

Shape

Answer 28

The center is the median and/or mean of the data. The spread is the range of the data. And, the shape describes the type of graph. The four ways to describe shape are whether it is symmetric, how many peaks it has, if it is skewed to the left or right, and whether it is uniform.

Question 29

Mode

Answer 29

The mode is the number that is repeated more often than any other.

Question 30

Center

Answer 30

The center of a distribution is the middle of a distribution. For example, the center of 1 2 3 4 5 is the number 3. … Look at a graph, or a list of the numbers, and see if the center is obvious.

Question 31

Spread

Answer 31

Measures of spread describe how similar or varied the set of observed values are for a particular variable (data item). Measures of spread include the range, quartiles and the interquartile range, variance and standard deviation.

Question 32

Range

Answer 32

In statistics, the range of a set of data is the difference between the largest and smallest values.

Question 33

Outlier

Answer 33

In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to variability in the measurement or it may indicate experimental error; the latter are sometimes excluded from the data set. An outlier can cause serious problems in statistical analyses.

Question 34

Symmetric

Answer 34

A symmetric distribution is a type of distribution where the left side of the distribution mirrors the right side. By definition, a symmetric distribution is never a skewed distribution. … The normal distribution is symmetric. It is also a unimodal distribution (it has one peak). Standard normal distribution.

Question 35

Skewed Right

Answer 35

A distribution that is skewed right (also known as positively skewed) is shown below. … For a right skewed distribution, the mean is typically greater than the median. Also notice that the tail of the distribution on the right hand (positive) side is longer than on the left hand side.

Question 36

Skewed Left

Answer 36

A distribution that is skewed left has exactly the opposite characteristics of one that is skewed right: the mean is typically less than the median; the tail of the distribution is longer on the left hand side than on the right hand side; and. the median is closer to the third quartile than to the first quartile.

Question 37

Unimodal

Answer 37

A unimodal distribution is a distribution with one clear peak or most frequent value. The values increase at first, rising to a single peak where they then decrease. … The normal distribution is an example of a unimodal distribution; The normal curve has one local maximum (peak).

Question 38

Multimodal

Answer 38

A multimodal distribution is a probability distribution with more than one peak, or “mode.” A distribution with one peak is called unimodal. A distribution with two peaks is called bimodal. A distribution with two peaks or more is multimodal.

Question 39

Stemplot

Answer 39

A stem and leaf plot is a way to plot data where the data is split into stems (the largest digit) and leaves (the smallest digits). … A very long leaf means that “stem” has a large amount of data.

Question 40

Splitting Stems

Answer 40

Split stems is a term used to describe stem-and-leaf plots that have more than 1 space on the stem for the same interval. Example would be 1 with leaves 1-4, and a 2nd 1 containing leaves 5-9.

Question 41

Back-to-Back Stem

Answer 41

Back-to-back stemplots are a graphic option for comparing data from two populations. The center of a back-to-back stemplot consists of a column of stems, with a vertical line on each side. Leaves representing one data set extend from the right, and leaves representing the other data set extend from the left.

Question 42

Plots

Answer 42

A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables.

Question 43

Histogram

Answer 43

A histogram is a bar graph-like representation of data that buckets a range of outcomes into columns along the x-axis. The y-axis represents the number count or percentage of occurrences in the data for each column and can be used to visualize data distributions.

Question 44

Mean

Answer 44

A mean score is an average score, often denoted by X. It is the sum of individual scores divided by the number of individuals.

Question 45

Median

Answer 45

The median is a simple measure of central tendency. To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

Question 46

Interquartile Range

Answer 46

The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles.

Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively.

For example, consider the following numbers: 1, 3, 4, 5, 5, 6, 7, 11. Q1 is the middle value in the first half of the data set. Since there are an even number of data points in the first half of the data set, the middle value is the average of the two middle values; that is, Q1 = (3 + 4)/2 or Q1 = 3.5. Q3 is the middle value in the second half of the data set. Again, since the second half of the data set has an even number of observations, the middle value is the average of the two middle values; that is, Q3 = (6 + 7)/2 or Q3 = 6.5. The interquartile range is Q3 minus Q1, so IQR = 6.5 - 3.5 = 3.

Question 47

Five-Number

Answer 47

The five-number summary is a set of descriptive statistics that provides information about a dataset.

Question 48

Summary

Answer 48

The information that gives a quick and simple description of the data. Can include mean, median, mode, minimum value, maximum value, range, standard deviation, etc.

Question 49

Boxplot

Answer 49

In descriptive statistics, a box plot or boxplot is a method for graphically depicting groups of numerical data through their quartiles. Box plots may also have lines extending from the boxes (whiskers) indicating variability outside the upper and lower quartiles, hence the terms box-and-whisker plot and box-and- …

Question 50

Standard Deviation

Answer 50

A quantity expressing by how much the members of a group differ from the mean value for the group.

Question 51

Variance

Answer 51

The variance is a numerical value used to indicate how widely individuals in a group vary. If individual observations vary greatly from the group mean, the variance is big; and vice versa.

It is important to distinguish between the variance of a population and the variance of a sample. They have different notation, and they are computed differently. The variance of a population is denoted by σ2; and the variance of a sample, by s2.

The variance of a population is defined by the following formula:

σ2 = Σ ( Xi - X )2 / N

where σ2 is the population variance, X is the population mean, Xi is the ith element from the population, and N is the number of elements in the population.

The variance of a sample is defined by slightly different formula:

s2 = Σ ( xi - x )2 / ( n - 1 )

where s2 is the sample variance, x is the sample mean, xi is the ith element from the sample, and n is the number of elements in the sample. Using this formula, the variance of the sample is an unbiased estimate of the variance of the population.

And finally, the variance is equal to the square of the standard deviation.