A group of 14- and 15-year-olds were polled on their favorite season. The results are shown in the frequency table.

| | 14 yr | 15 yr | Total |
|---------|-------|-------|-------|
| Summer | 23 | 22 | 45 |
| Spring | 5 | 3 | 8 |
| Fall | 7 | 7 | 14 |
| Winter | 12 | 3 | 15 |
| Total | 47 | 35 | |

1. How many categories are shown in the rows?
- Answer: [tex]$\square$[/tex]

2. How many categories are shown in the columns?
- Answer: [tex]$\square$[/tex]

3. How many 14-year-olds consider winter their favorite season?
- Answer: [tex]$\square$[/tex]

4. How many people total were polled?
- Answer: [tex]$\square$[/tex]



Answer :

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]

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