Statistics. Vocabulary

Transcription

1 Statistics Vocabulary

2 Qualitative Data - can be arranged into categories that are not numerical. It's also called Categorical Data. Quantitative Data - is numerical. It is acquired through counting or measuring.

3 Variables In statistics, a variable has two defining characteristics: 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.

4 Discrete vs. Continuous Variables If a variable can take on any value between two specified values, it is called a continuous variable; otherwise, it is called a discrete variable. Discrete and continuous variables are numeric.

5 Some examples will clarify the difference between discrete and continuous variables. 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. Suppose we flip a coin and count the number of heads. The number of heads would be an integer. We could not get 2.5 heads. Therefore, the number of heads must be a discrete variable.

6 Which of the following statements are true? I. All variables can be classified as quantitative or categorical variables. II. Categorical variables can be continuous variables. III. Quantitative variables can be discrete variables. (A) I only (B) II only (C) III only (D) I and II (E) I and III The correct answer is (E). All variables can be classified as quantitative or categorical variables. Discrete variables are indeed a category of quantitative variables. Categorical variables, however, are not numeric. Therefore, they cannot be classified as continuous variables.

7 How to describe data... Shape, Center, Spread

8 Shape Symmetry. When it is graphed, a symmetric distribution can be divided at the center so that each half is a mirror image of the other. Number of peaks. Distributions can have few or many peaks. Distributions with one clear peak are called unimodal, and distributions with two clear peaks are called bimodal. When a symmetric distribution has a single peak at the center, it is referred to as bell-shaped. Skewness. When they are displayed graphically, some distributions have many more observations on one side of the graph than the other. Distributions with fewer observations on the right (toward higher values) are said to be skewed right; and distributions with fewer observations on the left (toward lower values) are said to be skewed left. Uniform. When the observations in a set of data are equally spread across the range of the distribution, the distribution is called a uniform distribution. A uniform distribution has no clear peaks.

9 Shape Draw examples of each: Symmetrical Skew right Skew left Uniform Non-symmetric bimodal Symmetric bimodal

10

11 Center Graphically, the center of a distribution is located at the median of the distribution. This is the point in a graphic display where about half of the observations are on either side.

12 Spread The spread of a distribution refers to the variability of the data. If the observations cover a wide range, the spread is larger. If the observations are clustered around a single value, the spread is smaller.

13 Gaps and Outliers How do they affect mean and median?

14 Central Limit Theorem Statistics

15 Central Limit Theorem The Central Limit Theorem implies that, no matter what the population distribution looks like, the distribution of the sample means will approach a normal distribution. A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data.

16 Central Limit Theorem As the sample size increases, the sampling distribution of the mean,, can be approximated by a normal distribution with mean μ and standard deviation where: μ is the population mean, σ is the population standard deviation, n is the sample size x n

17 In other words... If we repeatedly take independent random samples of size n from any population, then when n is large, the distribution of the sample means will approach a normal distribution. When is n large enough? Generally, we need a sample size of 50 or more.

18 We re making a study We can't collect all the data from an entire population! We use a sample group

19 So, instead... Gather a subset of data (a sample group) from a population, and then use statistics for that sample to draw conclusions about the population.

20 We like normal distributions... Mean and standard deviation are used to define a population. When data follow a normal distribution, the mean indicates where the center of that distribution is, and the standard deviation reveals the spread.

21 The Central Limit Theorem implies that, no matter what the population distribution looks like, the distribution of the sample means will approach a normal distribution. We can make probability statements about the possible range of values the sample mean may take. Remember the Empirical Rule?