Let's break down the solution step-by-step:
We know the following:
- Total females surveyed: 150
- Total males surveyed: 450
- Total expert players: 80
- Total novice players: 180
First, we determine the number of novice females. From the information, we know there are 50 novice females.
Next, calculate the average females. Since there are 150 females evenly divided among the expertise levels, we divide 150 by 3, which gives us 50 average females.
Now, find the number of expert females. Since there are 80 expert players in total and we know there are 30 expert males, the remaining expert players must be females. Thus, expert females = 80 - 30 = 50.
Summarize the female distribution:
- Novice females: 50
- Average females: 50
- Expert females: 50
Next, let's calculate the total surveyed, which is the sum of all surveyed males and females: 450 + 150 = 600.
Now, let's calculate the number of average players in total. We know there are 80 expert players and 180 novice players, therefore total players = 600.
So, average players = total surveyed - expert players - novice players = 600 - 80 - 180 = 340.
Next, let's calculate males for each category. Knowing the following totals:
- Novice players: 180
- Expert players: 80
- Average players: 340
We previously calculated:
- Novice females: 50
- Expert females: 50
- Average females: 50
Hence:
- Novice males = 180 - 50 = 130
- Expert males = 30
Average males = 340 - 50 = 290
So, let's fill in the missing cells in the table:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline
& & \multicolumn{2}{|c|}{\text{Gender}} & \text{Total} \\
\hline \text{} & \text{} & \text{Male} & \text{Female} & \\
\hline \text{} & \text{Novice} & 130 & 50 & 180 \\
\hline \text{} & \text{Average} & 290 & 50 & 340 \\
\hline \text{} & \text{Expert} & 30 & 50 & 80 \\
\hline \text{} & \text{Total} & 450 & 150 & 600 \\
\hline
\end{array}
\][/tex]
This completes the table based on the given conditions.
