The stem and leaf diagram below shows the number of copies of the Newry News sold each week over 17 weeks in a particular shop - Junior Cycle Mathematics - Question 4 - 2017

The mode is the most frequently occurring number in the dataset. By reviewing the stem and leaf diagram:

• Stem 1: 6, 6, 7, 9, 9
• Stem 2: 0, 1, 5, 6, 8
• Stem 3: 2, 4
• Stem 4: 1, 7

The number 6 occurs twice, and 9 also occurs twice. Thus,

$\text{Mode} = 6 \text{ and } 9$

However, as we typically state the smallest mode in statistics, we conclude: $\text{Mode} = 6$

To find the median, we need to list the values in ascending order:

8, 6, 6, 9, 9, 20, 21, 25, 26, 28, 32, 34, 41, 47, 48, 49, 5 (for p=7)

Since there are 17 data points (odd number): the median is the middle value: $\text{Median} = \text{9th value} = 21$

To find the mean, we use the formula:

$\text{Mean} = \frac{\text{Sum of the data}}{\text{Number of data points}}$

Here the sum is given as 431, and there are 17 data points: $\text{Mean} = \frac{431}{17} = 25.35$

Rounding to one decimal place: $\text{Mean} = 25.4$

With 18 weeks and an additional number for the special issue, we consider sales of 19 copies, which occurs frequently.

Thus, keeping our previous mode as 6, the new mode remains: $\text{Modal Number} = 19$

To calculate the median for 18 values: In addition to the previous values listed, we include the new high value for the 18th week, which we assume is significantly high. This results typically changes the middle value. Using the new value calculations with median formula aligns at:

$\text{Median} = \frac{21 + x}{2}$ where $x$ = value of the added weeks.

Assuming x modifies values, say 23 (given from earlier): median's average reflects the sorted order into account. Using known figures, median rises: $\text{Median} = 23.0$

To find the number of copies sold in the 18th week, we use the mean:

Given the mean is 28.5 and total sales over 18 weeks: $\text{Total} = 18 \times 28.5 = 513$

From here, we subtract the total from previous weeks (431): $513 - 431 = 82$ Thus, copies sold in the 18th week is: $\text{Copies sold } = 82$