Question

Rank each set of data. $$ 11.7,18.6,41.7,11.7,16.2,5.1,31.4,5.1,14.3 $$

Short answer

5.1 = 1.5, 11.7 = 3.5, 14.3 = 5, 16.2 = 6, 18.6 = 7, 31.4 = 8, 41.7 = 9.

Step-by-step solution

List and Identify the Data

Start by noting down the given set of numbers: 11.7, 18.6, 41.7, 11.7, 16.2, 5.1, 31.4, 5.1, 14.3. Make sure you identify any repeating values, as ties need special consideration when ranking.

Order the Data in Ascending Order

Arrange the numbers from the smallest to the largest value: 5.1, 5.1, 11.7, 11.7, 14.3, 16.2, 18.6, 31.4, 41.7.

Assign Ranks to Ordered Data

Assign ranks starting from 1 for the lowest number. Since 5.1 repeats, assign both as rank 1.5 (the average of ranks 1 and 2). Similarly, both 11.7s receive rank 3.5 (the average of ranks 3 and 4). Continue assigning ranks to the rest of the numbers: 14.3 as 5, 16.2 as 6, 18.6 as 7, 31.4 as 8, and 41.7 as 9.

Key concepts

Understanding Ascending Order

To rank data effectively, the first step is organizing the values in ascending order. Simply put, this means arranging the numbers from smallest to largest.

For instance, if we have the numbers 11.7, 5.1, and 18.6, sorting them in ascending order would result in 5.1, 11.7, and 18.6.

Why is ascending order important? This arrangement helps us compare and rank the values more intuitively, as you're working from the lowest to the highest. Remembering this straightforward procedure is crucial for any ranking process.

Handling Ties in Ranking

Sometimes, in a list of numbers, certain values can repeat—these are called ties. When ranking data, ties require special attention to ensure fairness and accuracy.

Here's how you handle ties:

• Identify the repeated values.
• Instead of assigning them consecutive ranks, calculate the average of those ranks and assign the average rank to all tied values.

For example, if the values 11.7 and 11.7 appear in positions 3 and 4, find the average: \[ \frac{3 + 4}{2} = 3.5 \]In this way, both instances of 11.7 receive a rank of 3.5. Handling ties in this manner ensures that the ranking system reflects the actual data accurately and equitably.

Assigning Ranks

Once your data is organized in ascending order and you've resolved any ties, you're ready to assign ranks to each value.

This process begins with ranking the smallest value as 1. Simply continue assigning increasing ranks for each subsequent number.

When you encounter tied values, use the average rank as discussed. Consider the following sequence:

• 5.1, 5.1 (both receive rank 1.5)
• 11.7, 11.7 (both receive rank 3.5)
• 14.3 receives 5
• 16.2 as 6, 18.6 as 7, and so on

Assigning ranks like this ensures clarity and precision, helping make data analysis straightforward and meaningful.