MEASURES OF CENTRAL TENDENCY: UNGROUPED DATA / III. Measures of Variation/Dispersion Flashcards
- also called the average or central location in a data set or distribution
- A summary measure that describes a whole set of data with a single
value that represents the middle of its distribution.
MEASURES OF CENTRAL TENDENCY: UNGROUPED DATA
: listing or function showing all possible values of data and how often they occur
Distribution
: means data is raw that is not sorted or classified yet into categories. Ungrouped set of data basically a list of numbers
Ungrouped data
adding all the numbers or given data
Summation (∑x)
Three measures of central tendency
Mean. Median, Mode
: The total value of an observation in a data set
divided by the number of all observations.
Mean
the middle value in distribution when the values are arranged in ascending or descending order; if no middle: get the average of two middle numbers by adding and dividing by two
Median
The most commonly (frequent) occurring value in a distribution or data set. Sometimes distribution has no mode or more than one
mode
Mode
Types of mode:
o Unimodal – one mode
o Multimodal (more than one mode)
o Bimodal – 2 modes
o Trimodal – 3 mode
Data management:
❖ Measures of Variation
❖ Measures of Position
- A measure of variability/variation
- Level of consistency.
- It is used to describe the distribution of the data
How is the data distributed?
* cluster
* spread out
Measures of Variation/Dispersion
o It is the simplest measure of variation.
o It is greatly affected by extreme values and it is not resistant to change since it only uses the largest and smallest values.
o Not a good measure of variability.
o can be obtained by subtracting the lowest score from the highest score.
o Formula = Highest Value – Lowest Value
Range
o Is the average of how much the data values differ from the mean.
o No negative Sign
o Small MAD value = clustered data values.
o Big MAD value = spread out data values.
Mean Absolute Value
− it is a reliable measure of dispersion and is widely used in modern educational statistics and educational experiments
− use to determine how far or clustered a random data points from their average value
Variation
− it is also a reliable measure of dispersion
− it is the square root of variance
− it is used to quantify the amount of variation or dispersion of a set of data
− Formula:
Sample = 𝒔𝒅 = √𝒔²
Population = 𝜎 = √𝜎²
where: 𝒙 ̅- mean, x – data
Standard Deviation
− It determines the position of a single value in relation to other values in a sample
of population data set.
− also called fractiles
− It is a score distribution where the scores are divided into different equal parts
Quantiles
− a measure of position that divides the ordered observations or score distribution into 4 equal parts
− it is the th score
❖ QUARTILES (k=1-4)
− a measure of position that divides the ordered observations or score distribution
into 10 equal parts
− it is the th score
DECILE (k = 1-10)
− a measure of position that divides the ordered observations or score
distribution
into 100 equal parts
− it is the th score
PERCENTILE (k = 1-100)
- − Another way of measuring the variability of an observation
QUANTILE DEVIATION
