Question

*3.
number of goals scored by
a soccer team in 29 games
based on the graph above, in how many of the games
played did the soccer team score goals equal to the
median number of goals for the 29 games?

Explanation:

Step1: Find the median position

For \( n = 29 \) (odd number of games), the median is the \(\frac{n + 1}{2}=\frac{29+1}{2}=15^{\text{th}}\) value when the data is ordered.

Step2: Cumulate the frequencies

• Goals = 0: Let's assume the height (number of games) is 1 (from the graph, the bar for 0 is up to 1). Cumulative: \( 1 \)
• Goals = 1: Bar height is 8. Cumulative: \( 1 + 8 = 9 \)
• Goals = 2: Bar height is 9. Cumulative: \( 9 + 9 = 18 \)

Since the \( 15^{\text{th}} \) value falls within the goals = 2 category (because \( 9 < 15 \leq 18 \)), the median number of goals is 2.

Step3: Find the number of games with 2 goals

From the graph, the bar for goals = 2 has a height of 9, so the number of games with 2 goals (the median number of goals) is 9.

Answer:

9