Descriptive Statistics: An Introduction to Data Analysis | Summaries Business Statistics

Discriptive Statistics

Statistics is much more than just computing averages. Statistics provides the means of gaining

insight—both numerically and visually—into large quantities of data, understanding uncertainty and

risk, and drawing conclusions from sample data that come from very large populations.

For example, marketing analysts employ statistics extensively to analyze survey data to understand

brand loyalty and satisfaction with goods and services, to segment customers into groups for

targeted ads, and to identify factors that drive consumer demand; finance personnel use statistics to

evaluate stock and mutual fund performance in order to identify good investment opportunities and

to evaluate changes in foreign currency rates.

Descriptive statistics refers to methods of describing and summarizing data using tabular, visual, and

quantitative techniques.

A metric is a unit of measurement that provides a way to objectively quantify performance. For

example, senior managers might assess overall business performance using such metrics as net

profit, return on investment, market share, and customer satisfaction.

Measurement is the act of obtaining data associated with a metric. Measures are numerical values

associated with metric.

Metrics can be either discrete or continuous. A discrete metric is one that is derived from counting

something. For example, a delivery is either on time or not; an order is complete or incomplete.

Continuous metrics are based on a continuous scale of measurement.Any mertic involving dollar,

length, time, volume, or weight, for example, are continuous.

Another classification of data is by the type of measurement scale. Data may be classified into four

groups:

1. Categorical (nominal) data, which are sorted into categories according to specified

characteristics. For example, a firm’s customers might be classified by their geographical

region (e.g., North America, South America, Europe, and Pacific); employees might be

classified as managers, supervisors, and associates. The categories bear no quantitative

relationship to one another, but we usually assign an arbitrary number to each category to

ease the process of managing the data and computing statistics. Categorical data are usually

counted or expressed as proportions or percentages.

2. Ordinal data, which can be ordered or ranked according to some relationship to one

another. College football or basketball rankings are ordinal; a higher ranking signifies a

stronger team but does not specify any numerical measure of strength. ordinal data are

more meaningful than categorical data because data can be compared. ,ordinal data have no

fixed units of measurement.

3. Interval data, which are ordinal but have constant differences between observations and

have arbitrary zero points. Common examples are time and temperature. Time is relative to

global location, and calendars have arbitrary starting dates (compare, for example, the

standard Gregorian calendar with the Chinese calendar)

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Discriptive Statistics Statistics is much more than just computing averages. Statistics provides the means of gaining insight—both numerically and visually—into large quantities of data, understanding uncertainty and risk, and drawing conclusions from sample data that come from very large populations. For example, marketing analysts employ statistics extensively to analyze survey data to understand brand loyalty and satisfaction with goods and services, to segment customers into groups for targeted ads, and to identify factors that drive consumer demand; finance personnel use statistics to evaluate stock and mutual fund performance in order to identify good investment opportunities and to evaluate changes in foreign currency rates. Descriptive statistics refers to methods of describing and summarizing data using tabular, visual, and quantitative techniques. A metric is a unit of measurement that provides a way to objectively quantify performance. For example, senior managers might assess overall business performance using such metrics as net profit, return on investment, market share, and customer satisfaction. Measurement is the act of obtaining data associated with a metric. Measures are numerical values associated with metric. Metrics can be either discrete or continuous. A discrete metric is one that is derived from counting something. For example, a delivery is either on time or not; an order is complete or incomplete. Continuous metrics are based on a continuous scale of measurement.Any mertic involving dollar, length, time, volume, or weight, for example, are continuous. Another classification of data is by the type of measurement scale. Data may be classified into four groups:

Categorical (nominal) data, which are sorted into categories according to specified characteristics. For example, a firm’s customers might be classified by their geographical region (e.g., North America, South America, Europe, and Pacific); employees might be classified as managers, supervisors, and associates. The categories bear no quantitative relationship to one another, but we usually assign an arbitrary number to each category to ease the process of managing the data and computing statistics. Categorical data are usually counted or expressed as proportions or percentages.
Ordinal data, which can be ordered or ranked according to some relationship to one another. College football or basketball rankings are ordinal; a higher ranking signifies a stronger team but does not specify any numerical measure of strength. ordinal data are more meaningful than categorical data because data can be compared. ,ordinal data have no fixed units of measurement.
Interval data, which are ordinal but have constant differences between observations and have arbitrary zero points. Common examples are time and temperature. Time is relative to global location, and calendars have arbitrary starting dates (compare, for example, the standard Gregorian calendar with the Chinese calendar)

4.. Ratio data, which are continuous and have a natural zero point. Most business and economic data, such as dollars and time, fall into this category. For example, the measure dollars has an absolute zero. Ratios of dollar figures are meaningful. FREQUENCY DISTRIBUTION N HISTOGRAMS: frequency distribution is a table that shows the number of observations in each of several nonoverlapping groups. A graphical depiction of a frequency distribution in the form of a column chart is called a histogram. Frequency distributions and histograms summarize basic characteristics of data, such as where the data are centered and how broadly data are dispersed. PERCENTILES AND QUARTILES : Data are often expressed as percentiles and quartiles. Percentiles specify the percent of other test takers who scored at or below the score of a particular individual. Generally speaking, the kth percentile is a value at or below which at least k percent of the observations lie. kth percentile using the formula nk /100 + 0.5. where n is the number of observations. Round this to the nearest integer, and take the value corresponding to this rank as the kth percentile. Quartiles break the data into four parts. POPULATION AND SAMPLES : A population consists of all items of interest for a particular decision or investigation—for example, all individuals in the United States who do not own cell phones, all subscribers to Netflix, or all stockholders of Google. Most populations, even if they are finite, are generally too large to deal with effectively or practically. A sample is a subset of a population. MEASURES OF LOCATION :MEAN ,MEDIAN ,MODE ,MIDRANGE Arithmetic Mean: The average is formally called the arithmetic mean (or simply the mean), which is the sum of the observations divided by the number of observations. One property of the mean is that the sum of the deviations of each observation from the mean is zero.

MEASURES OF DISPERSION:RANGE ,INTERQUARTILE RANGE,VARIANCE ,STANDARD DEVIATION

Dispersion refers to the degree of variation in the data, that is, the numerical spread (or compactness) of the data. RANGE: formula =MAX(data range) - MIN(data range) VARIANCE : A more commonly used measure of dispersion is the variance, whose computation depends on all the data. The larger the variance, the more the data are spread out from the mean and the more variability one can expect in the observations.

STANDARD DEVIATION ;

The standard deviation is the square root of the variance. For a population, the standard deviation is computed as,

Descriptive Statistics: An Introduction to Data Analysis, Summaries of Business Statistics

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MEASURES OF DISPERSION:RANGE ,INTERQUARTILE RANGE,VARIANCE ,STANDARD DEVIATION

STANDARD DEVIATION ;