Let's break this down step by step:
1. Number of Categories in the Rows:
The rows represent different seasons. In the frequency table, these seasons are:
- Summer
- Spring
- Fall
- Winter
Thus, the number of categories shown in the rows is:
[tex]\[ \text{Number of Row Categories} = 4 \][/tex]
2. Number of Categories in the Columns:
The columns represent different age groups and the total. In the frequency table, these categories are:
- 14 yr
- 15 yr
- Total
So, the number of categories shown in the columns is:
[tex]\[ \text{Number of Column Categories} = 3 \][/tex]
3. Number of 14-year-olds who consider winter their favorite season:
We look at the entry in the Winter row and the 14 yr column. From the table, this number is:
[tex]\[ \text{14-year-olds who prefer Winter} = 12 \][/tex]
4. Total Number of People Polled:
Finally, to find the total number of people polled, we sum all the entries under the 14 yr and 15 yr columns. The individual entries are for both age groups:
[tex]\[ 23 + 22 + 5 + 3 + 7 + 7 + 12 + 3 = 82 \][/tex]
Therefore, the total number of people polled is:
[tex]\[ \text{Total Polled} = 82 \][/tex]
So, the answers are:
[tex]\[ \text{Number of Row Categories} = 4 \][/tex]
[tex]\[ \text{Number of Column Categories} = 3 \][/tex]
[tex]\[ \text{14-year-olds who prefer Winter} = 12 \][/tex]
[tex]\[ \text{Total Polled} = 82 \][/tex]
