Measures of Dispersion for
Ungrouped Data
MEASURES Of DISPERSION:
It is also called a measure of variability, it describes the spread of the
individual distribution from the average. Among the measures are the range, variance,
and standard deviation.
Range - the simplest and easiest way to determine among the measure of dispersion. It
is the difference between the highest value and the lowest value in the data set.
Advantages:
1. It is easy to compute.
2. It is easy to understand.
Disadvantages:
1. It can be distorted by a single extreme value.
2. Only two values are used in the calculation.
Examples:
1. Find the range of the ages of 9 middle management employees of a certain company. The
ages are 53, 45, 59, 48, 54, 46, 51, 58 and 55.
, Solution:
Given: HV = 59
LV = 45
Answer: R = 59 - 45
R = 14
2. The following data represent the total unit sales for smartphones from a sample of 10
Communication Centers for August: 15, 17, 10, 12, 13, 10, 14, 10, 8, and 9. Find the range.
Solution:
Given: HV = 17
LV = 8
Answer: R = 17 - 8
R=9
Variance and Standard Deviation
Standard Deviation is considered one of the most widely used measures of
dispersion. The more spread the data the higher the deviation. It is a statistical term that
provides a good indication of volatility. It measures how widely values are dispersed
from the average. It is computed as the square root of the variance.
Variance is the measure of the dispersion of a set of data points around the
mean value. It is the average of the squared deviation of the values about the mean.
Vitality is the measure of risk, it can help determine the investor might take in
purchasing a specific security.
The following are the formula to be used in solving the variance and standard deviation
of ungrouped data given a sample or a population.
1. The formula for Sample Variance ( denoted by s2s2)
and Sample Standard Deviation ( denoted by s )
Ungrouped Data
MEASURES Of DISPERSION:
It is also called a measure of variability, it describes the spread of the
individual distribution from the average. Among the measures are the range, variance,
and standard deviation.
Range - the simplest and easiest way to determine among the measure of dispersion. It
is the difference between the highest value and the lowest value in the data set.
Advantages:
1. It is easy to compute.
2. It is easy to understand.
Disadvantages:
1. It can be distorted by a single extreme value.
2. Only two values are used in the calculation.
Examples:
1. Find the range of the ages of 9 middle management employees of a certain company. The
ages are 53, 45, 59, 48, 54, 46, 51, 58 and 55.
, Solution:
Given: HV = 59
LV = 45
Answer: R = 59 - 45
R = 14
2. The following data represent the total unit sales for smartphones from a sample of 10
Communication Centers for August: 15, 17, 10, 12, 13, 10, 14, 10, 8, and 9. Find the range.
Solution:
Given: HV = 17
LV = 8
Answer: R = 17 - 8
R=9
Variance and Standard Deviation
Standard Deviation is considered one of the most widely used measures of
dispersion. The more spread the data the higher the deviation. It is a statistical term that
provides a good indication of volatility. It measures how widely values are dispersed
from the average. It is computed as the square root of the variance.
Variance is the measure of the dispersion of a set of data points around the
mean value. It is the average of the squared deviation of the values about the mean.
Vitality is the measure of risk, it can help determine the investor might take in
purchasing a specific security.
The following are the formula to be used in solving the variance and standard deviation
of ungrouped data given a sample or a population.
1. The formula for Sample Variance ( denoted by s2s2)
and Sample Standard Deviation ( denoted by s )
