Business Stats Test 1

Relative Frequency Distribution shows

the fraction or percentage of observations in each class interval

Advantage of stem and leaf over frequency distribution

the identity of each observation is not lost and helps better understand the distribution

Median

the midpoint of the values after they have been ordered from the minimum to the maximum values

5 statistics needed to construct a box plot

the min value Q1 the median Q3 the max value

Quantitative Variable

information is reported numerically ex: balance in your checking account, minutes remaining in class

An advantage of a cumulative frequency polygon over a histogram

it can show the total number of observations up to a particular class boundary

Advantage of the standard deviation over the variance

it is in the same units as the data

the advantage of standard deviation over the variance

it is in the same units as the data

Mode

the value of the observation that appears most frequently

Raw Data

ungrouped data which is to be organized into a frequency distribution

Properties of median

unique for each data set not affected by extremely large or small values valuable measure of central tendency can be computed for an open-ended frequency distribution

Why does sample variance use one less than sample size

use of sample size tends to underestimate the population variance and subtracting one corrects this

What is the purpose of a measure of location

'to pinpoint the center' of a distribution data

What characteristic of a data set makes the median the best measure of the center of the data?

One or two very large or very small values

Quantitative Variable Classification

Discrete and Continuous

Box Plot

A graphical display, based on quartiles, that helps us picture a set of data

Shape

characteristic of distribution

Coefficient of skewness range

-3 up to 3

Formula to determine the number of classes

2^k>n

Steps to Relative Frequency Table

Divide the data into classes Count the observations Calculate the fraction of observations in each class

Pie Chart

A chart that shows the proportion or percent that each class represents of the total number of frequencies

Inferential Statistics

A decision, estimate, prediction, or generalization about a population based on a sample.

Bar Chart

A graph that shows qualitative classes on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are proportional to the heights of the bars

Histogram

A graph which the classes are marked on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars.

Frequency Table

A grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class

Frequency Distribution

A grouping of quantitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class

Parameter

A measurable characteristic of a population, such as the mean or dispersion

Statistic

A measurable characteristic of a sample

Two major characteristics of mean

ALL values are used the sum of deviations from the mean is 0

Frequency Polygon

Consists of line segments connecting the class midpoints of the class frequencies

Frequency Distribution Steps

Decide the # of classes Determine class width Set individual class limits Tally the # of observations in each class

Three measures of location

Arithmetic mean Median Mode

Measures of location are referred to as

Averages

Relative Frequency

Captures the relationship between a class total and the total number of observations

Empirical Rule

For a symmetrical, bell-shaped frequency distribution, approximately 68% of the observations will lie within plus and minus one standard deviation of the mean; about 95% of the observations will lie within plus and minus two standard deviations of the mean; and practically all (99.7%) will lie within plus and minus three standard deviations of the mean.

Common Displays of Frequency Distribution

Histograms Frequency Polygons Cumulative Frequency Distributions

Types of Variables

Qualitative and Quantitative

Measures of position

Quartiles Deciles Percentiles

Three measures of dispersion

Range, Variance, Standard Deviation

Mode is especially useful in summarizing what kind of data

Nominal-level

Class Interval

Obtained by subtracting the lower limit of a class from the lower limit of the next class

Which two of the following practices is commonly used in setting class limits for a frequency distribution?

Placing "excess" interval width equally in the two tails of the distribution Rounding the class size up

Stem-and-leaf Display

Statistical Technique used to display quantitative info leading digit=stem(vertical) trailing digit=leaf(horizontal)

Two ethical approaches to the use of statistics

requires objective and honest communication of results must maintain independent and principled point of view

Arithmetic Mean

requires the interval scale and is calculated by summing the values and dividing by the # of values

Class Midpoint

The average of the upper and lower limits of two consecutive classes

Class Frequency

The number of observations in each class

Dispersion

The variation/spread in data

Negatively Skewed Distribution

There are a small number of observations that are much lower in value than most of the data

A frequency table shows what kind of data

qualitative (nominal)

Population

a collection of all possible individuals, objects, or measurements of interest

Sample

a portion, or part, of the population of interest

In sample variance, dividing by n-1 corrects what

a tendency to underestimate population variance

A frequency distribution groups..

quantitative data into classes showing the number of observations per class

What kind of data is shown in a histogram

quantitative data/variables (interval or ratio level)

Ratio Level

all quantitative data. the highest level of measurement. data classifications are ordered according to the amount of the characteristics they possess. equal differences in the characteristics are represented by equal differences in the numbers assigned to classifications

two reasons to study dispersion

allows the comparison of the spread in two or more distributions a small value for dispersion indicates that the data is closely clustered around the center

To divide data with a high value of H and a low value of L into k classes, the interval must be

at least (H-L)/k

Continuous Variable

can assume any value within a specified range ex: the pressure in a tire, the height of students in a class

Discrete Variables

can only assume certain values and there are usually "gaps" between values ex: the number of bedrooms in a house

Ordinal Level

data arranged in some order, but the differences between the data values cannot be determined or are meaningless data classified can be ranked or ordered

Interval Level

data classifications are ordered according to the amount of the characteristics they possess equal differences in the characteristic are represented by equal differences in the measurements

Nominal Level

data that is classified into categories and cannot be arranged in any particular order

Level of Measurement

dictates the calculation that can be done to summarize and present the data. used to determine the statistical tests that should be performed on the data

example of ordinal

during a taste test of 4 soft drinks, mellow yellow was ranked number 1, sprite number 2, seven up 3, orange 4

Convert a frequency distribution to relative frequency

each class frequency is divided by total number of observations

A frequency distribution displays info of what level of data

ratio (quantitative)

example of nominal

eye color, gender, religious affiliation

Population Mean

for ungrouped data the sum of all the population values divided by the total number of population values

Sample mean

for ungrouped data, is the sum of all the sample values divided by the number of sample values

Dot plots

groups the data as little as possible and the identity of an individual observation is not lost each observation is displayed as a dot along the horizontal # line used for smaller sets of data

Formula to determine the class interval/width

i>_ (H-L)/k

Histogram has what advantage over the frequency polygon

it shows the class width directly as a rectangle with the height representing the # of observations

Three weaknesses of the Range

may be unduly influenced by an unusually large value may be unduly influenced by an especially small value only two values from the data set are used

Why is dispersion important

measures of location do not tell us about the spread or clustering of data

what is the best measure of "average" income in a country where most of the households have annual incomes of about 40,000 but a small number of households have incomes above 1,000,000

median

Descriptive Statistics

methods of organizing, summarizing, and presenting data in an informative way

example of ratio

monthly income of surgeons, or distance traveled by manufacturers representatives per month

three reasons the mode is not a good measure of average

no observation occurs more than once the data is bimodal the most frequent observation is much higher or lower than most of the data values

Four levels of measurement

nominal, interval, ordinal, ratio

"frequency" in a frequency distribution refers to what

number of "observations" in each of the classes into which the data is divided

Mean and standard deviation calculation for grouped data is..

only an estimate of the corresponding actual value

Variance

overcomes the problem of negative deviations by squaring them uses all of the values in a data set

a relative frequency converts the class frequency to what

percentage or proportion

Why take sample instead of population

prohibitive cost of census, destruction of item being studied may be required, not possible to test or inspect all member of a population being studied

What kind of data can a median be computed for

ratio, interval, and ordinal

4 Shapes

symmetric positively skewed negatively skewed bimodal

dispersion

tells us about the spread of data

example of interval

temperature of the Fahrenheit scale, womens dress sizes

How is the number of observations for each class plotted on a frequency distribution table

the # on the vertical axis and the class midpoint on the horizontal axis

Zero Point

the absence of the characteristic and the ratio between two numbers is meaningful. ratio level data

Qualitative Variable

the characteristic being studied is nonnumeric ex: gender, religion, type of automobile owned, state of birth, eye color

What info is on the vertical axis of a bar chart

the class and relative class frequencies

when is the mode used to measure the "average" of a set of data

the data is symmetrically distributed but has one very high value

Weighted mean

the denominator is always the sum of the weights used with data that has repeated values, such as frequency distribution

Range

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

Sample Standard Deviation

used as an estimator of the population standard deviation

Weighted Mean

used with data that has repeated values denominator is always the sum of the weights

Geometric Mean

useful in finding the average change of percentages, ratios, indexes, or growth rates over time *will always be less than or equal to the arithmetic mean

Piled on dots

when there are identical observations that are too close to be shown individually, the dots are piled on top of each other