Some Internet service providers (ISPs) charge companies...

Some Internet service providers (ISPs) charge companies based on how much bandwidth they use in a month. One method that ISPs use for calculating bandwidth is to find the 95th percentile of a company's usage based on samples of hundreds of 5 -minute intervals during a month. (a) Explain what "95th percentile" means in this selting. (b) Which would cost a company more: the 9th percentile method or a similar approach using the 98 th percentile? Justify your answer.

Some Internet service providers (ISPs) charge companies based on how much bandwidth they use in a month. One method that ISPs use for calculating bandwidth is to find the 95th percentile of a company's usage based on samples of hundreds of 5 -minute intervals during a month. (a) Explain what "95th percentile" means in this selting.
(b) Which would cost a company more: the 9th percentile method or a similar approach using the 98 th percentile? Justify your answer.

Key Concepts

Percentile

A percentile is a statistical measure indicating the value below which a given percentage of observations in a group fall. For example, the 95th percentile is the value below which 95% of the sampled data points lie, providing a way to understand the distribution of data by focusing on a particular slice of the data set.

ISP Bandwidth Billing Using Percentile Methods

This concept refers to the billing strategy where an Internet service provider calculates a customer’s bandwidth usage based on the percentile of usage samples rather than the absolute average or peak usage. This method is used to avoid charging for brief spikes in usage that occur infrequently, by selecting a high percentile (such as the 95th) which excludes the top 5% of usage intervals.

Data Sampling for Usage Measurement

Data sampling involves collecting usage data at regular intervals (such as every 5 minutes) over a monitoring period. This systematic approach allows ISPs to gather a sufficient number of data points to accurately calculate percentiles and assess typical usage patterns while filtering out anomalous spikes.

Impact of Percentile Threshold Selection

The percentile threshold chosen (for example, 95th versus 98th) directly affects the billing amount. A higher percentile threshold, such as the 98th percentile, takes into account a larger portion of the high-usage samples and thereby results in a higher value compared to a lower threshold like the 9th percentile, which would not capture peak usage and would therefore cost less. This illustrates how different thresholds impact the evaluation of bandwidth usage and billing costs.

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