The Median for Ungrouped Data
To find the median of ungrouped data, the values or measurements must be arranged in an array. It may be either in an increasing or a decreasing oreder. Then we get the value or the measurement in the middle. If there is an even number of values, then the two values in the middle are added together then divided by two.
Median
The median is another measure of central tendency. It is the middle value of a given set of measurements, when the values or measurements are arranged in an array.
An array is an arrangement of values in increasing or decreasing order.
Below are the characteristics of the mean of any distribution:
1. The mean is the most appropriate measure of central tendency when the data are in the interval or ratio scale.
2. The mean lies between the largest and smallest values or measurements.
3. There is only one value for the mean for a given set of values or measurements.
4. The mean is easily influenced by extreme values because all values contribute to the average. If there are high values, the mean tends to be high also. If there are extremely low values, the mean tends to be low also.
where:
Xam = assumed mean
f = frequency
d = coded deviation
n = total frequency
i = class size
The formula for the mean using the classmark is as follows:
where:
x = measurement or score
f = frequency
X = classmark
n = total frequency
Mean for Grouped Data
To compute the mean for grouped data, we can use two formulas, namely:
1. The Classmark Formula, and
2. The Coded Formula.
4.1: Mean - Weighted Arithmetic Mean
There are sets of values where the values or measurements involved have different “weights” or degree of importance. The mean of this set is called a “weighted mean.” The formula for computing a weighted mean is as follows:
where:
= mean
x = measurement or value
W = weight
Sample Mean - mean of ungrouped or raw data
= meanMean - the sum of all the measurements in a data set divided by the number of measurements in the set; the symbol for mean is .
Although text, tables and graphs effectively present data, these do not sufficiently describe the data being presented.
Measures of Central Tendency - numerical descriptive measures which indicate the center of a data set
There are three commonly used measures of central tendency: