For AI agents: use /llms.txt for the Nakafa content index.
To calculate the mean:
Mean formula:
The quantities in this formula are:
We will compare the mean, median, and mode of the same data set before and after adding two unusually large values.
Initial situation:
Ten members of School A's student council collect wearable clothes for a community drive. The number of items collected by each member is:
Finding the initial mean, median, and mode:
Sort the data (for the median and mode):
(there are , )
Calculate the mean:
Find the median:
The number of data points is even (). The middle data are at positions and .
Find the mode:
The most frequent values are () and ().
So, the initial modes are and (bimodal).
New situation:
The next day, joined and donated and items of clothing.
The new data becomes:
Finding the new mean, median, and mode:
Sort the data:
(there are , )
Calculate the new mean:
Find the new median:
The number of data points is even (). The middle data are at positions and .
Find the new mode:
The most frequent values are still () and ().
So, the new modes are and .
Compare the measures of central tendency before and after the two values are added:
Adding and , two values far above the original data, has the largest effect on the mean. The larger values pull the mean upward.
The median also changes, but less sharply. The mode does not change at all.
Replace the th student's donation with , then recalculate the mean to measure the effect of this unusually large value.
Data becomes: ()
Calculate the mean:
The mean becomes , far above both the initial mean () and the previous mean ().
Find the median:
Sorted data:
The median is still , the same as before.
Find the mode:
Mode remains and .
An extreme value may be classified as an outlier under a stated statistical rule or through domain judgment. In this example, strongly affects the mean but leaves the median and modes unchanged. This sensitivity is the mean's main weakness. The median and mode are more stable when one unusually large or small value appears.
The mean is easy to calculate, but an unusually large or small value can make it less representative of the rest of the data.
Published: . Updated: .
So, the initial mean is .
The value at position is , and the value at position is .
So, the initial median is .
So, the new mean is .
The value at position is , the value at position is .
So, the new median is .
