Let's analyze the stem and leaf diagram to determine the given values.
Based on the diagram and the key provided, we can interpret the scores Harri achieved:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
& 8 & & & & & \\
\hline
1 & 1 & 1 & 5 & 7 & 8 & \\
\hline
2 & 0 & 2 & 3 & 3 & 4 & 7 \\
\hline
3 & 4 & 4 & 4 & 6 & 9 & \\
\hline
\end{array}
\][/tex]
The scores from the diagram are:
- 81, 81, 85, 87, 88
- 90, 92, 93, 93, 94, 97
- 100, 103, 103, 104, 106, 109
a) Range of scores:
To find the range of the scores, we'll subtract the smallest score from the largest score.
- The smallest score is 81.
- The largest score is 109.
Now, compute the range:
[tex]\[
\text{Range} = 109 - 81 = 28 \text{ points}
\][/tex]
b) Modal score:
The mode is the score that appears most frequently in the list. By observing the scores:
- 81 appears twice.
- 93 appears twice.
- 103 appears twice.
Out of these, the smallest score appearing most frequently (first observed mode) is 81.
Thus:
- The modal score is 81 points.
Overall, the answers are:
a) Range of scores: [tex]\( 28 \)[/tex] points
b) Harri's modal score: [tex]\( 81 \)[/tex] points
