Chapter 1-4 Statistics Frequency Distribution And Population

In this chapter we discuss statistics frequency distribution and population.


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


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


a numerical characteristic of a sample


the characteristic about which we are interested


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


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


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


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


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


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


population mean – parameter


physical center of a data set


the most frequently occurring value in a data set


when two values occur with the same greatest frequency


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


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


Within 2 Standard Deviations


Within 3 Standard Deviations


Measures of Relative Standing

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


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


divide an ordered data set into four equal parts

Five-Number Summary

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

Interquartile Range



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


theoretical probability


empirical probability

Sample Space

the set of all possible outcomes of an experiment

Sample Points

the individual outcomes in a sample space


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)