A group of students was asked how many text messages each had sent the previous day - Junior Cycle Mathematics - Question 13 - 2013

To create a stem-and-leaf diagram, we separate each number into a stem (the first digit or digits) and a leaf (the last digit). Here’s how the data can be organized:

Stem | Leaf
0    | 3 6 7 9
1    | 1 4 5 6 7 8 9
2    | 2 5 8 8
3    | 1 2 5
4    | 0 2

Key: 2 | 5 = 25

The mode is the number that appears most frequently in a set of data. From the data provided:

The numbers are: 6, 7, 9, 11, 14, 15, 16, 17, 18, 19, 25, 28, 28, 32, 34, 35, 40, 42.

Here, the number 28 appears twice, which is more than any other value. Therefore, the mode of the data is 28.

To find the mean, we sum all the values and divide by the total number of values.

Sum: 14 + 32 + 6 + 17 + 19 + 15 + 3 + 35 + 42 + 25 + 9 + 28 + 34 + 18 + 40 + 11 + 16 + 28 + 31 + 7 = 430.

The total number of students is 20. Therefore the mean is calculated as:

$$ext{Mean} = \frac{430}{20} = 21.5$$

To find the percentage of students who sent more than 30 texts, we first count the number of students who fall into this category:

The values greater than 30 are: 32, 35, 40, and 42. This makes a total of 6 students.

Now, we calculate the percentage:

$$\frac{6}{20} \times 100 = 30\%$$

Thus, 30% of the students sent more than 30 texts.