Question

find the mode of this stem - and - leaf plot. key: 0 | 5 means 5

Explanation:

Step1: Understand stem - leaf plot

In a stem - leaf plot, the stem is the left - hand column and the leaf is the right - hand column. The key tells us how to interpret the numbers. For example, \(0|5\) means 5, \(1|0\) means 10, \(1|2\) means 12, \(2|1\) means 21.
So we first list out all the data points from the stem - leaf plot:

• For stem 0: leaves are 5, 7, 8. So the data points are 5, 7, 8.
• For stem 1: leaves are 0, 2, 2, 5. So the data points are 10, 12, 12, 15.
• For stem 2: leaf is 1. So the data point is 21.

The complete data set is: \(5,7,8,10,12,12,15,21\)

Step2: Find the mode

The mode of a data set is the value that appears most frequently. We count the frequency of each number:

• \(5\): appears 1 time.
• \(7\): appears 1 time.
• \(8\): appears 1 time.
• \(10\): appears 1 time.
• \(12\): appears 2 times.
• \(15\): appears 1 time.
• \(21\): appears 1 time.

Since 12 appears more frequently (2 times) than any other number, the mode is 12.

Answer:

The mode of the data represented by the stem - and - leaf plot is 12.