记录了 14 名学生完成一份数学作业所花费的时间（以分钟为单位）。结果如茎叶图所示。

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完整解法

1. Find the value with the highest frequency

From the stem-and-leaf diagram, the times include
$23, 23, 23$ .

No other time appears more than twice, so the modal time is $23$ minutes.

答案

$23$ mins

1. Identify students who took at most 20 minutes and calculate the percentage

Times at most $20$ minutes are $11, 15, 19, 20$ , so there are $4$ students.

Total number of students $=14$ .

$\frac{4}{14}\times 100\%=28.571\ldots\%=28.6\%$

答案

$\dfrac{3}{14}\times 100\%=21.4\%$

1. Find the original smallest and greatest times

From the stem-and-leaf diagram, the smallest time is $11$ minutes and the greatest time is $40$ minutes.

Original range $=40-11=29$ minutes.

2. Find the possible new times that make the new range 31 minutes

The new range is $31$ minutes.

If the new time is the new smallest value, then
$40-x=31$
$x=9.$

If the new time is the new greatest value, then
$x-11=31$
$x=42.$

答案

$9$ mins or $42$ mins

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