MEASURES OF CENTRAL TENDENCY, DISPERSION, LOCATION Flashcards
Method of compressing mass of data for better comprehension and description
Summarizing Figures
Make use of the measures of central tendency, dispersion, and location
Summarizing Figures
Mean, median, and mode
Have the typical values; all values that represent all the observations
Measures of Central Tendency
range, variance, and standard deviation
Describe the variability of observations
Measures of Dispersion
percentile, decile and quartile
Shows relative position of an observation in an array
Measures of Location
Tells us where the values tend to clump but not measure the spread of variability of data
Measures of Central Tendency
AKA measures of central location
A single value that attempts to describe a set of data by identifying the central position within that set of data
Measures of Central Tendency
Measures of Central Tendency:
is the sum of the values of observations divided by the number of observations.
Sum of the observations ÷ number of observations
Mean
average
Measures of Central Tendency:
Sensitive to different/ extreme observations; any change in the observation will change the mean value
Mean
Sum of the deviations of the observations from the mean is equal to zero
Point of balance or center of gravity of the distribution
Measures of Central Tendency:
Most popular and well known measure of central tendency
Mean
Used for discrete and continuous data
X: designate an _____
i: designates ______
𝛴: ______
X̅: _______
observation
position of an observation
summation notation
sample mean
μ: ______
N: # of items in the _____
n: # of items in the _____
population mean
population
sample mean
Measures of Central Tendency:
The middle score for a set of data that has been arranged in order of magnitude
Median
(Odd: middle most observation
Even: mean of 2 middlemost observation)
Measures of Central Tendency:
Middle most observation in a set of observations put in numerical order in an array (ascending or descending)
Median
Not influence by outliers
Measures of Central Tendency:
The most frequently occurring value in a set of observation
Mode
can be determined for any type of variable
Measures of Central Tendency:
Used for categorical data, to know which is the most common category
Mode
Locations of Measures of Central Tendency: Types of Distribution:
Negatively skewed
Right to left
Mean is less than the median and mode
Negative Direction
Locations of Measures of Central Tendency: Types of Distribution:
Normal (no skew), Center
Perfectly Symmetrical Distribution
Locations of Measures of Central Tendency: Types of Distribution:
Positively skewed
Left to right
Mode is less than the median and mean
Positive Direction
Best Measure of Central Tendency: Nominal : \_\_\_\_\_ Ordinal : \_\_\_\_\_ Interval/ Ratio (no skewed) : \_\_\_\_\_\_ Interval/ Ratio (skewed) : \_\_\_\_\_
Mode
Median
Mean
Median
Measures the spread of variability of data
Measures of Dispersion aka Measures of Spread
Used to describe the variability in a sample or population used in conjunction with a measure of central tendency
Measures of Dispersion
May be used for quantitative variables only
Describe whether the population or sample is homogeneous or heterogeneous
Measures of Dispersion
range, variance, standard deviation, and coefficient variation
Measures of Dispersion
Measures of Dispersion:
Difference between the highest and lowest value, can measure the spread or variability
Range
simplest measure of dispersion
Measures of Dispersion:
Used when you have ordinal data
Range
Measures of Dispersion:
The average of the squared deviations from the mean
Measure of variability that takes the mean as the reference point
Variance
Units are incomprehensible
Measures of Dispersion:
Square root of the variance
Unit is the same as that of the original set of observations
Standard Deviation
squared deviations
Measures of Dispersion:
Measure of relative variation. Always a %
Expresses the SD as % of mean
Coefficient of Variation
SD ÷ Mean x 100
Measures of Dispersion:
Shows variation relative to Mean
Used to compare 2 or more groups
Coefficient of Variation (CV)
Determines the location/ position of a particular value in an array of distribution
Provide more details about a part of the entire distribution of observations in a give data
Measures of Location
Used for both qualitative and quantitative data
Quartiles, deciles, percentiles
Measures of Location
Measures of Location:
Points of distribution that divides the observation into 100 equal parts
Percentiles: Pi
1 of the 99 values of a variable which divides the distribution into 100 equal parts
Measures of Location:
Points of distribution that divides the observation into 10 equal parts
1 of the 9 values of a variable which divides the distribution into 10 equal parts
Deciles: Di
Decile to Percentile: D1= P10
Measures of Location:
Points of distribution that divides the observation into 4 equal parts
1 of the 3 values of a variable which divides the distribution into 4 equal parts
Quartiles: Qi
Quartile to Percentiles: Q1= P25
What is Q3 in percentile?
P75 or 75th percentile
1 quartile = 25 percentile
What is Q2 in decile?
D5 or 5th decile
What is P60 in decile?
D6 or 6th decile
10 percentile = 1 decile
What is P25 in quartile?
Q1 or 1st quartile
25 percentile = 1 quartile
What is Q2 in percentile?
P50 or 50th percentile
1 quartile = 25 percentile