Let's break the questions down step by step.
1. How many categories are shown in the rows?
- The frequency table provided includes four different rows corresponding to the seasons: Summer, Spring, Fall, and Winter. Therefore, the number of categories shown in the rows is:
[tex]\[
\boxed{4}
\][/tex]
2. How many categories are shown in the columns?
- The table has three main columns for the age categories: 14-year-olds, 15-year-olds, and Total. Since we are interested in distinct age categories, not including the 'Total' column, there are two categories shown in the columns:
[tex]\[
\boxed{2}
\][/tex]
3. How many 14-year-olds consider winter their favorite season?
- According to the data in the table, in the Winter row under the 14-year column, the number is 12. Therefore, the number of 14-year-olds who consider winter their favorite season is:
[tex]\[
\boxed{12}
\][/tex]
4. How many people total were polled?
- To find the total number of people polled, we need to add up the '14 yr' and '15 yr' columns:
- Total 14-year-olds: 23 (Summer) + 5 (Spring) + 7 (Fall) + 12 (Winter) = 47
- Total 15-year-olds: 22 (Summer) + 3 (Spring) + 7 (Fall) + 3 (Winter) = 35
- Adding these sums gives the total number of people polled:
[tex]\[
47 + 35 = 82
\][/tex]
Hence, the total number of people who were polled is:
[tex]\[
\boxed{82}
\][/tex]
