DESCRIPTIVE STATISTICS CHAPTER 2: MEASURE OF CENTRAL TENDENCY

Standard deviation

is a number used to tell how measurements for a group are SPREAD OUT FROM THE AVERAGE (mean or expected value).

CV or the coefficient of variation

is a statistical measure of the DISPARITY (a difference in level) of data points in a data set around the mean.

Median

it is the positional average

Mean, Median and the Mode

One important measure used to describe a whole set of data with a single value that represents the middle or center of its distribution is the

MEDIAN

______ is the positional average. There is a need to organize first the data from lowest to highest, before we can get the "middle score or value".

Outliers

are EXTREME, or atypical data value(s) that are notably different from the rest of the data.

Negative

A kurtosis value that is NEGATIVE shows a LIGHT TAILS which means that there are little amount of data in the tails of a distribution

positive

A kurtosis value that is ____ pictures a HEAVY TAILS- that is there are a lot of data in the tail part of the distribution

Standard Deviation

A quantity calculated to indicate the extent of DEVIATION for a group as a whole. =stdev(highlight the data sets)

MEAN

Also known as the ARITHMETIC MEAN, is the most reliable measure of central tendency. Operationally, it is derived by adding up all the observed values divided by the total number of observed values

mean

As the ____ includes every value in the distribution the mean is influenced by outliers and skewed distributions.

good

CV is 10-20

Acceptable

CV is 20-30

very good

CV is <10

not acceptable

CV>30

relative dispersion of data

Coefficient of Variation is sometimes called?

LEPTOKURTIC

More values in the distribution tails and more values close to the mean (i.e. sharply peaked with heavy tails) • Having greater kurtosis than the normal distribution; more concentrated about the mean. Coefficient of K > 3

discrete variable

_____ is a numeric variable. Observations can take a value based on a count from a set of distinct WHOLE VALUES.

coefficient of variation

represents the ratio of the standard deviation to the mean,

SD

tandaan, kapag greater ABSOLUTE dispersion, saan ang icocompare, mean or standard deviation?

Mean

tandaan, kapag greater RELATIVE dispersion, saan ang icocompare, mean or standard deviation?

median

the _____ cannot be identified for categorical NOMINAL data, as it cannot be logically ordered.

median

the preferred measure of central tendency when the distribution is NOT SYMMETRICAL.

continuous

variable is a NUMERIC VARIABLE. Observations can take any value between a certain set of REAL NUMBERS.

Skewed to the left (Negatively skewed)

when the tail on the left side of the distribution is longer than the right side.

Skewed to the right (Positively skewed)

when the tail on the right side of the distribution is longer than the left side

CV

-volatility -variability

symmetrical - normal skewed to the right - positively skewed skewed to the left - negatively skewed

REMEMBER:

continuous and discrete

The MEAN can be both use for?

MESOKURTIC

A distributions that are moderate in breadth and curves with a medium peaked height.

MESOKURTIC

A distributions that are moderate in breadth and curves with a medium peaked height. It is described to be normal. K = 3

Variance

It measures how far a set of numbers is SPREAD out from their average value. =standard devation^2

Skewed to the right (Positively skewed)

In this case, the mean is higher than the Median and the mode. Then median tends to be higher than the mode. MEAN ---> MEDIAN ----> MODE

Skewed to the right (Positively skewed) (2)

In this case, the mean is higher than the Median and the mode. Then median tends to be higher than the mode. The mean is 'pulled' toward the right tail of the distribution. COEFFCIENT OF SKEWNESS > 0 (meme)

Skewed to the right (positively skewed) (2)

In this case, the mean is less than the Median and the mode. Then mode is higher than the median. The mean is 'PULLED' toward the RIGHT tail of the distribution. Coefficient of sk < 0

Kurtosis

It describes the SHARPNESS of the peak of a frequency distribution curve.

CV or the coefficient of variation

It is a useful indicator of COMPARISON on the differences of one data series to another, even if the means are drastically different from one another.

A low standard deviation means that most of the numbers are close to the average, while a high standard deviation means that the numbers are more spread out.

REMEMBER:

A small variance indicates that the data points tend to be very close to the mean, and to each other. A high variance indicates that the data points are very spread out from the mean, and from one another. Variance is the average of the SQUARED distances from each point to the mean.

REMEMBER:

median

The ____ is LESS affected by OUTLIERS and SKEWED data than the mean, and is usually the preferred measure of central tendency when the distribution is not symmetrical.

Skewed to the left (Negatively skewed)

The mean is 'pulled' toward the left tail of the distribution.

Range (2)

The___ is the simplest measure of variation. Operationally, it measures the distance between the highest observed value from the smallest observed value.

PLATYKURTIC

This is characterized by a distributions that have NEGATIVE kurtosis. The tails are very thin compared to the normal distribution, resulting in fewer extreme positive or negative events. Coefficient of K < 3

Range

This value indicates "how far are the 2 extreme values" ? = H - L 'Max minus Min"

Range

This value indicates "how far are the 2 extreme values" Range = H - L 'Max minus Min"

SYMMETRICAL DISTRIBUTION

When the mean, median and the mode becomes equal, then the distribution assumed normality. It is said to be symmetrical or balanced. COEFFICIENT OF SKEWNESS = 0

normality

When the mean, median and the mode becomes equal, then the distribution assumed? It is said to be symmetrical or balanced.

Measures of Variation

gives us the information on how data in a given distribution are being DISPERSED or SPREAD. • It also described how similar or varied the set of observed values

Categorical variables

have values that describe a 'QUALITY' or 'CHARACTERISTIC' of a data unit, like 'what type' or 'which category'.

Numeric variables

have values that describe a measurable quantity as a number, like 'HOW MANY' or 'HOW MUCH'.

numbers are more spread

high average standard deviation = ?

MODE

is a central measure that refers to MOST FREQUENT data in a given distribution.

Kurtosis

is a measure of the "tailedness" of the probability distribution of a real-valued random variable. It describes the sharpness of the peak of a frequency- distribution curve.

Skewness

is the tendency for the values to be more frequent around the high or low ends of the x-axis.

Skewness (2)

is the tendency for the values to be more frequent around the high or low ends of the x-axis.

close to average or close to mean

low standard deviation = ?