Summary Report - Group 2
AÑASCO, JELORD
BATUCAN, MARCEL DION
BERAME, MAECHEL
Descriptive Statistics: Numerical Measures
MEASURES OF CENTRAL TENDENCY
A measure of central tendency, commonly referred to as an average, is a single value that
represents a data set. Its purpose is to locate the center of a data set.
THREE DIFFERENT MEASURES OF CENTRAL TENDENCY
○ Mean
○ Median
○ Mode
MEAN
The arithmetic mean or often called as the mean is the frequently used measure of central
tendency. In which all values plays an equal role, meaning, to determine its value you would need to
consider all the values of any given data set.
Properties of Mean:
1. A set of data has only one mean.
2. Mean can be applied for interval and ratio data.
3. All values in the data set are included in computing the mean.
4. The mean is very useful in comparing two or more data set.
5. Mean is affected by the extreme small or large value on a data set.
6. Mean is more appropriate in symmetrical data.
Mean = Sum of all values/Number of values
Types of Mean
Sample Mean and Population Mean
MEDIAN
The median is the midpoint of the data array. When the data set is ordered, whether ascending or
descending, it is called data array.
1. The median is unique, there is only one median for a set of data.
2. The median is found by arranging the set of data from lowest to highest or vice versa and getting
the value of middle observation.
3. Median is not affected by the extreme small or large values.
4. Median can be applied for ordinal, interval and ratio data.
5. Median is most appropriate in skewed data.
MODE
The value in the data set that appears the most frequently. A data may not contain any mode if none
of the values are “ most typical”
TYPES OF MODE
Unimodal - A data set that has only one value that occurs the greatest frequency.
Bimodal - If the data has two (2) values with the same greatest frequency.
Multimodal - If a data set has more than two modes.
WEIGHTED MEAN
The weighted mean equation is a statistical method that calculates the average by multiplying the
weights with their respective mean and taking its sum. It is a type of average in which the weights
assign individual values to determine the relative importance of each observation.
SHAPE OF A DISTRIBUTION
● Describes how data are distributed
● Two useful shape related statistics are:
○ Skewness - Measures the extent to which data values are not symmetrical
○ Kurtosis - Kurtosis affects the peakedness of the curve of the distribution—that is,
how sharply the curve rises approaching the center of the distribution.
MEASURES OF RELATIVE POSITION
The Measure of Relative Position is a statistical method used to determine where an observation
falls in relation to a set of data. The most common example in education is the conversion of scores
on standardized tests to show where a given student stands in relation to other students of the
same age, grade level, etc.
Quartiles
Quartiles are values that divide a data set into quarters after the data set has been ordered.
Where:
● Q1 = splits the lowest 25% of the sorted data
● Q2 = splits the lowest 50% of the sorted data (MEDIAN)
● Q2 = splits the lowest 75% of the sorted data
When calculating the ranked position use the
following rules:
● If whole number, then it is the ranked position to use.
● If fractional half, then average the two corresponding data values.
● If neither the two, then round the result to the nearest integer.
Percentiles
Percentiles indicate the percentage of data outcomes in a set which fall under a certain value. It
divides the whole data set into a hundred equal parts.
Percentiles formula:
Example:
Sidney is taking a biology course in university. She got a mark of 78% and the list of all marks from
her class (including her mark) is given by {56, 83, 74, 67, 47, 54, 82, 78, 86, 90}.
● What percentile did she score in?
● Sidneys friend Billy knows he got in the 70th percentile, what was his mark?
Solutions:
Step 1: Arrange the data in ascending order.
{47, 54, 56, 67, 74, 78, 82, 83, 86, 90}
Step 2: Solve for the percentile.
So we have that Sidney scored in the 50th percentile (or above the 50%).
Billy's mark: Solve for the score.
Therefore, there are 7 data values in the set before Billys score, which means Billy got a 83% in
his Biology course.
MEASURES OF VARIATION
The measure of variation give information on the spread or variability or dispersion of the data
values.
Range
Range is the difference of the highest value and the lowest value in the data set. It is probably the
simplest and easiest way to determine measure of dispersion.
● Does not account for how the data are distributed
Example:
The daily rates of a sample of 8 employees at GMS Inc. are 550, 420, 560, 500, 700, 670, 860, 480.
Find the range.
Solution:
Step 1: Determine the highest value and lowest value in the data set.
Highest Value (HV) = 860
Lowest Value (LV) = 420
Step 2: Solve for the range.
Range = HV - LV
Range = 860 - 420 = 440
The range in daily rate salary is 440.
Interquartile Range
A measure of variability is the difference between the third quartile, Q3, and the first quartile, Q1. In
other words, the interquartile range is the range for the middle 50% of the data.
IQR = Q3 – Q1
Example:
The data on monthly starting salaries, the quartiles are Q3 = 3600 and Q1 = 3465. Thus, the
interquartile range is 3600 – 3465 = 135.
Variance
Variance is a measure of the spread or dispersion of data points in a dataset. It is calculated by
taking the average of the squared differences between each data point and the mean. Variance is
expressed in square units of the original data.
Example:
10 ,8, 10, 8, 8, 4
Mean: 8
Variance: 4.8
Standard Deviation
Standard deviation is also a measure of the spread or dispersion of data points, but it is the square
root of the variance. It measures the average distance of data points from the mean. Standard
deviation is expressed in the same units as the original data, making it easier to interpret compared
to variance.
Example:
10, 8, 10, 8, 8, 4
Mean: 8
Variance: 4.8
Standard Deviation: 2.19
