JOEBERT M.
ACIERTO
Ped-6 Group-2
Sir Montegrande
1. The properties of Mean?
The mean minimize error in the prediction of any one value in the data set.
The mean need not be an integer even if all the elements of the collection are
integers
Explain: The mean is the sum of all the elements of a collection divided by the number
of elements in the collection. The mean need not be an element of the collection, and it
need not be an integer even if all the elements of the collection are integers.
Explain: The mean minimizes the sum of squared errors, which means that it minimizes
the error in the prediction of any one value in the data set.
The sum of squared errors is the sum of the squared differences between each value in
the data set and the mean. The mean is the value that minimizes this sum of squared
errors, and it is the unique estimate that does so.
The mean minimizes the mean squared error (MSE), which is a common measure of
estimator quality.
The MSE is a quadratic function of the estimate, and the minimizing value of the estimate
is the mean.
Therefore, the mean is the best estimate of the data set, and it minimizes the error in the
prediction of any one value in the data set.
2. The properties of median?
The median is the middle value in a data set when the values are arranged in
ascending or descending order.
The median is not affected by all of the data values in a dataset
Explain: The median is not affected by all of the data values in a dataset. This means
that changing one data value does not necessarily affect the median, unless the data
value is moved across the middle of the data set. Every change in a data value affects
the mean, but not the median. The median value is fixed by its position and is not reflected
by the individual value.
Explain: The median is the middle value in a data set when the values are arranged in
ascending or descending order, if the data set has an odd number of observations, the
middle value is selected as the median. For example, in the data set -1, 3, 5, 7, 9, the
median is 5. If the data set has an even number of observations, there is no distinct
middle value, and the median is usually defined to be the arithmetic mean of the two
middle values. For example, in the data set 1, 2, 3, 4, the median is (2+3)/2 = 2.5. The
median is not affected by extreme values or outliers in the data set, making it a useful
measure of central tendency in skewed distributions or when outliers are present
The median is a special case of other ways of summarizing the typical values associated
with a statistical distribution: it is the 2nd quartile, 5th decile, and 50th percentile
3. Properties of mode?
The mode is the value that occurs most frequently in a data set.
The mode can be used to deal with qualitative variables.
Explain: The mode is a measure of central tendency that represents the value that
occurs most frequently in a data set. One of the properties of the mode is that it can be
used to deal with qualitative variables. Qualitative variables are variables that are not
numerical and fit the data into categories.
Explain: The mode is a measure of central tendency that represents the most frequently
occurring value in a data set
It is the value that appears most often in the data set. A data set may have one mode,
more than one mode, or no mode at all
Data, such as the most common color or flavor. It is the only measure of central tendency
for nominal variables, where it can reflect the most commonly found characteristic
The mode is not affected by extreme values or outliers in the data set, making it a
valuable tool for summarizing data sets
However, the mode can be ill-defined if the maximum frequency is repeated or if the
maximum frequency occurs either at the very beginning or at the end of the distribution,
or if the distribution is irregular
The mode is the easiest to compute and can be used for open-ended distribution and
qualitative data
1. Five applications of mean are?
Business:
Explain: The mean is frequently used in all aspects of business, such as the
number of items produced, sales, and profits
Statistics and data analysis:
Explain: The mean is an essential tool in statistics and data analysis. It is used
to interpret or summarize the given data set and derive relevant information or
conclusions about the population or sample of a population represented by the
data set
Academic studies:
Explain: The mean is used in academic studies to analyze data and draw
conclusions
Geographical studies:
Explain: The mean is used in geographical studies to analyze data and draw
conclusions
Agricultural experiments:
Explain: The mean is used in agricultural experiments to analyze data and draw
conclusions
2. Five applications of median are?
Poverty line calculation:
Explain: The median is used in the calculation of the poverty line. It is a more
appropriate measure of central tendency than the mean when the data is
skewed and extreme values are present
Academic studies:
Explain: The median is used in academic studies to analyze data and draw
conclusions
Business:
Explain: The median is used in business to analyze data and draw conclusions,
such as the median salary of employees
Geographical studies:
Explain: The median is used in geographical studies to analyze data and draw
conclusions, such as the median income of a region
Medical research:
Explain: The median is used in medical research to analyze data and draw
conclusions, such as the median age of patients with a particular disease
3. Five applications of mode are?
Business:
Explain: The mode is used in business to analyze data and draw conclusions,
such as the most popular product or service
Education:
Explain: The mode is used in education to analyze data and draw conclusions,
such as the most common grade or score
Medical research:
Explain: The mode is used in medical research to analyze data and draw
conclusions, such as the most common symptom or diagnosis
Demographics:
Explain: The mode is used in demographics to analyze data and draw
conclusions, such as the most common age or gender
Quality control:
Explain: The mode is used in quality control to ensure that products or services
meet a certain standard, such as the most common defect in a product
