### Chapter 1-4 Statistics Frequency Distribution And Population

In this chapter we discuss statistics frequency distribution and population.

**Population**

the entire collection of individuals or objects about which information is desired. may be considered to be finite or infinite

**Census**

a collection of data from every member of the population

a sub-collection or subset of a population selected for study

a numerical characteristic of a population

**Statistic**

a numerical characteristic of a sample

**Variable**

the characteristic about which we are interested

**Data**

the observations that have been collected

**Qualitative Data**

categorical or attribute data

**Quantitative Data**

numerical data

**Discrete Data**

count dataquantitative)

**Continuous Data**

measure dataquantitative)

**Sampling Error**

the difference between the result of a sample and the result for the entire population. caused by random fluctuations of the sample- i.e. by chance

**Normal**

bell-shaped distribution

**Statistically Significant**

observation that is extremely unlikely to happen simply by chance

**Descriptive Statistics**

the collection, presentation, and description of data

**Inferential Statistics**

interpreting the data in order to draw conclusions about the population, based on information obtained from a sample

**Frequency Distribution**

a chart or table giving the values of a variable together with their corresponding frequencies

**Blood Type**

example of a frequency distribution for qualitative data

**Class Width**

the difference between two consecutive lower class boundaries

**Class Midpoints**

the center value of each class

**Relative Frequency**

a proportional measure of frequency, calculated by dividing the frequency of that class by the total frequency of the data set

**Pie Chart**

a circular graph showing the relationships of parts to a whole, only one variable at a time may be displayed

**Bar Graph**

a rectangular graph representing quantities using heights of detached rectangles, generally used to display qualitative or discrete data, displays an ungrouped frequency distribution

**Histogram**

a rectangular graph representing quantities using heights of attached rectangles, used to display continuous data, displays a grouped frequency

**Elements of a Histogram**

a title, a horizontal scaleidentifying the variable), a vertical scaleidentifying frequencies)

**Stem and Leaf Display**

combines graphing and sorting the data, split into the leading digits, the trailing digits

**Outlier**

an unusually large or small data value with respect to its data set

**Dotplot**

a number line above which each data value is plotted as a point

**Measures of Central Tendency**

the middle or center of a data set, averages- mean, median, mode, midrange

**Averages**

mean, median, mode, midrange

**Arithmetic Mean**

adding the data values and dividing by the number of data values, balance point of a data set

**X Bar**

sample mean – statistic

**Mu**

population mean – parameter

**Median**

physical center of a data set

**Mode**

the most frequently occurring value in a data set

**Bimodal**

when two values occur with the same greatest frequency

**Midrange**

the value midway between the lowest and highest values in a data set, L+H/2

**Measures of Dispersion**

measure the spread or variability of the data set

**Range**

the difference between the largest and smallest values in a data set

**Standard Deviation**

the average distance of the data values from their mean

**Within 1 Standard Deviation**

68%

**Within 2 Standard Deviations**

95%

**Within 3 Standard Deviations**

99.7%

**Measures of Relative Standing**

indicates the position of a data value in terms of its data set

**Z-Score**

gives the position of a data value in terms of standard deviations from its mean

**Quartiles**

divide an ordered data set into four equal parts

**Five-Number Summary**

Lowmin), Q1, medianQ2), Q3, and highmax)

**Interquartile Range**

Q3-Q1

**Probability**

______ that an event will occur is the relative frequency with which that event can be expected to occur

**P**

theoretical probability

**P’**

empirical probability

**Sample Space**

the set of all possible outcomes of an experiment

**Sample Points**

the individual outcomes in a sample space

**Event**

any subset of a sample space

**A Complement**

the set of all sample points in the sample space that do not belong to A

**Compound Event**

any event made up of two or more sample events

**P(A or B)**

probability that either A or B occurs

**Mutually Exclusive**

events cannot happen at the same time

**General Addition Rule**

P(A or B) = P(A) + P(B) – P(A and B)