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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?
- [tex]$\square$[/tex]

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

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

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

Sagot :

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]