Q:
# What Is the Formula for Finding the Median of Ungrouped Data?

Assuming the data has N elements in order of magnitude, the median is found by taking the ((N+1)/2)th element if there are an odd number of elements. If there are an even number of elements, then the median is an average of the (N/2)th and (N/2 + 1)th element.

Continue Reading
Credit:
moodboard
Cultura
Getty Images

To determine the median of ungrouped data with N elements, one should first order the data from lowest to highest. The median is determined by finding either the middle element in the data or the average of the middle two elements, depending on whether there are an odd or even number of elements in the data.

For example, suppose a set of data has the numbers {4, 8, 7, 10, 100}. First, one would reorder the elements from lowest to highest so that it appears as {4, 7, 8, 10, 100}. There are an odd number of elements in the set; i.e. N=5. Since (5+1)/2 = 3, in this case, the third element in the set is the median, which is 8.

Suppose the ordered data set has a sixth element of 1000, so it now looks like {4, 7, 8, 10, 100, 1000}. In this case, N=6; therefore N/2=3 and N/2 + 1 = 4, so the median is the average of the third and fourth data element. The median is (8 + 10)/2 = 9.

Learn more about Algebra-
Q:
## How Do You Calculae the Mean Absolute Deviation?

A: Find the mean absolute deviation by finding the sum of the absolute value of x minus mu, all divided by N. In this formula, mu is the mean, x is the value ... Full Answer >Filed Under: -
Q:
## How Do You Find the Cube of a Number?

A: In order to find the cube of a number, multiply the number by itself three times. A cube is expressed in exponential form as B^3, which is read as B cubed ... Full Answer >Filed Under: -
Q:
## What Are Some Distinguishable Permutations?

A: Examples of distinguishable permutations often include letter order in words, such as the number of ways in which the letters in the word "Mississippi" can... Full Answer >Filed Under: -
Q:
## What Is the Difference Between Grouped and Ungrouped Frequency Distributions?

A: In a grouped frequency distribution, data is sorted and separated into groups called classes, whereas in an ungrouped frequency distribution, a listing is ... Full Answer >Filed Under: