Business Statistics

Histogram

A graph in 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 and the bars are drawn adjacent to each other. Pg 35

Bar Chart

A graph in which the classes are reported on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are proportional to the heights of the bars

Weighted Mean

Each value is weighted according to its relative importance. For example, if 5 shirts cost $10 each and 20 shirts cost $8 each, the weighted mean price is $8.40 [ (5X10) + (20X8)/25= 216/25 = $8.40

Properties of the Arithmetic Mean

Every set of interval- or ratio level data has a mean. All the values are included in computing the mean. The mean is unique. The sum of the deviations of each value from the mean is zero

Percentiles

MOD that divides a set of observations into a hundred equal parts.

Nominal Level

gives you the least information. When observations of a qualitative variable can only be classified and counted. If data is classified into categories and the order of those categories is not important, it is the nominal level of measurement. EX: Gender and percentages

Your Savior with the numerical problems

https://www.khanacademy.org/math/probability

Deciles

is a MOD that divides a set of observations into 10 equal parts

Box Plot

is a graphical display, based on quartiles, that helps us picture a set of data. To construct a box plot (pg 111) we need only five statistics" the minimum value Q1, the median, Q3, and the maximum value.

Quartiles

measures of dispersion that divides a set of observations into four equal parts.

Positively skewed or Negatively skewed

pg 68

Classical Probability

probability based on the assumption that each of the outcomes is equally likely.. According to this concept of probability, if there are n possible outcomes, the probability of a particular outcome is 1/n. Thus, on the toss of a coin, the probability of a head is 1/n=1/2.

Variance

the arithmetic mean of the squared deviation from the mean

population

the collection or set of all individuals , objects, or measurements whose properties are being studies.

Symmetric

the observation's mean and median are equal and the data values are evenly spread around these values.

Statistics

the science of collecting, organizing, analyzing, and interpreting numerical data for the purpose of making more effective decisions.

Class interval

the size of each class into which a range of a variable is divided, as represented by the divisions of a histogram or bar chart. Subtract the lower limit of the clss from the lower limit of the next class.

Standard deviation

the square root of the variance

Arithmetic Mean

the sum of the values divided by the number of values. The symbol for the mean of a sample is X bar and the for a population mean is Mu

General rule of addition

used to find the probabilities of complex events made up of A or B when the events are not mutually exclusive.

General rule of multiplication

used to find the probabilities of events A and B both happening when the events are not independent. Example: it is known that there are 3 defective radios in a box containing 10 radios. What is the probability of selecting defective radios on the first two selections from the box? Where P(B|A) is the conditional probability and means "the probability of B occurring given that A has already occurred."

Ordinal Level

when one classification is "higher" or "better" than the next one. The zero point is arbitrary. Data classifications are represented by sets of labels or names (high, medium, low) that have relative values. Because of the relative values the data classified can be ranked into order

Skewed to the right or positively

when there is a single peak and the values extend much further to the right of the peak than to the left of the peak. In this case the mean is larger than the median.

Bimodal distribution

will have two or more peaks

Ratio Level

All qualitative data is recorded on the ratio level. Data classified are ordered according to the amount of the characteristic they posses. Equal differences in the characteristics are represented by equal differences in the measurements. The zero point is the absence of the characteristic and the ratio between two numbers is meaningful.

Experiment

An activity that is either observed or measured. An experiment may be counting the number of correct responses to a question, for example.

Relative Class Frequencies

Converting the class frequencies to RCF to show the fraction of the total number of observations in each class. To convert a frequency distribution to a relative frequency distribution, each class frequency is divided by the total number of observations.

Interval Level

Contains all the values of the ordinal level but in addition the difference between values is a constant size. Data classified are ordered according to the amount of the characteristic they posses. Equal differences in the characteristics are represented by equal differences in the measurements.

Long review on pg 142

...

Summary of chapter three pg

89 and 90 READ THIS EVERY DAY

Parameter

A characteristic of a population

Pie Chart

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

Event

A collection of one or more outcomes of an experiment. For example, an event is the collection of even numbers in the roll of a fair die.

Empirical Probability

A concept of probability based on the past experienc. For example, Metropolitan Life Insurance Company reported that, during the year, 100.2 of every 100,000 persons in Wyoming died of accidental causes (motor vehicle accidents, falls, drowning, firearms etc). On the bais of this experience, Metropolitan can estimate the proability of accidental death for a particular person in Wyoming: 100.2/100,000= 0.001002

Dot plot

A dot plot summarizes the distribution of one variable by stacking dots at points on a number line that shows the values of the variable. A dot plot shows all values.

Permutation Formula

A formula to count the number of possible outcomes when the outcomes is important. I a, b, c, is one arrangement, b, a, c another, c, a, b another, and so on, the total number of arrangements is determined by nPr

Combination Formula

A formula to count the possible outcomes when the order of the outcomes is not important. EX: if the order of abc, bac, or cba doesn't matter in the arrangements its considered a combination.

Frequency Distribution

A grouping of data into mutually exclusive classes showing the number of observations in each class. Go to page 28 for directions to construct a frequency distribution

Frequency Table

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

Outcome

A particular or measurement of an experiment

Mutually Exclusive

A property of a set of categories such that an individual, object, or measurement is included in only one category.

Measure of Dispersion

A single value that shows the spread of a data set. The range, variance, and standard deviation are measures of location.

Stem=And-Leaf Display

A statistical technique to present a set of data. Each numerical value is divided into two parts. The leading digits becomes the stem and the trailing digit the leeaf. The stems are located along the vertical axis, and the leaf values are stacked against each other along the horizontal axis. For example, if a data set contains the values between 13 and 84, eight classes base on the 10s digit would be used for the stems. The 1st digit would be the leaves.

Scatter Diagram

A statistical technique used to show the relationship between two variables.

Contingency Table

A table used to classify observations according to two identifiable characteristics

Probability

A value between 0 and 1, inclusive, that reports the likelihood that a specific event will occur.

Special rule of addition

For this rule to apply, the events must be mutually exclusive. For two events the probability of A or B occurring is found by : P(A or B)= P(A) + P(B) Example: the probability of a one=spot or a two spot occurring on the toss of one die P(A or B) = 1/6 + 1/6 = 2/6 = 1/3

Subjective rule of multiplication

If two events are not related- that is, they are independent - this rule is applied to determine the probability of their joint occurrence. P(A and B) = P(A)P(B) Example: the probability of two heads on two tosses of a coin is: P(a and B) = P(A)P(B)= 1/2 X 1/2 = 1/4

Chapter 3

Measures of location and measures of dispersion. Measures of location are averages. Measures of dispersion are called the variation or the spread in data.

Multiplication Formula

One of the formulas used to count the number of possible outcomes of an experiment.It states that there are m ways of doing on thing, and n ways of doing another, there are m X n ways of doing both. Example: a men's clothier offers two sport coats and three contrasting pants for $400. How many different outfits can there be. Answer: m X n = 2 X 3 = 6

A frequency polygon

Pg 37 Similar to a histogram, it consists of line segments connecting the points formed by the intersections of the class midpoints and the class frequencies.

Mean Deviation

The arithmetic mean of the absolute values of the deviations from the arithmetic mean. Abbreviated as MD

Subjective Probability

The chance of an event happening based on whatever information is available- hunches, personal opinions of others, rumors, and so on.

Interquartile range

The distance between the first and the third quartile. Q1 -> Q3. The The absolute numerical difference between the first and third quartile.

Class

The interval in which the data are tallied. For example, $4 up to $7 is a class; $7 up to $11 is another class

Conditional Probability

The likelihood that an event will occur given that another event has already occured

Negatively skewed or left

The mean is smaller than the median.

Coefficient of skewness

The measure of a lack of symmetry in a distribution. For a symmetric distribution there is no skewness, so the coefficient of skewness is zero. Otherwise it is either positive or negative, with the limits of

Class midpoint

The midpoint is halfway between the lower limits of two consecutive classes. Add the lower limits of consecutive classes and dividing the result by 2.

Median

The midpoint of the values after they have been ordered from the smallest to the largest, or the largest to the smallest.

Geometric Mean

The n-(th) root of the product of all the values. It is especially useful for averaging rates of change and index changes. It minimizes the importance of extreme values. A second use of the geometric mean is to find the mean annual percent change over a period of time. For example, if gross sales were $245 million in 1985 and $692 million in 2007, what is the average annual percent increase.

Class Frequency

The number of observations in each class

Independent

The probability that one event has no effect on the probability of another event

Mode

The value of the observation that appears most frequently. For grouped data, it is the midpoint of the class containing the largest number of values.

Measure of Location

a Value that is typical of the data. It pinpoints the center of a distribution. The arithmetic mean, weighted mean, median, mode, and geometric mean are measures of central location

Statistic

a characteristic of a sample

Sample

a portion of subset of the population being studied