Answered

The two-way table represents data from a survey asking teachers whether they teach English, math, or both.

| | English | Not English | Total |
|-----------|---------|-------------|-------|
| Math | 34 | 22 | 56 |
| Not Math | 40 | 8 | 48 |
| Total | 74 | 30 | 104 |

Which is the joint relative frequency for teachers who teach math and not English? Round the answer to the nearest percent.



Answer :

GinnyAnswer
To find the joint relative frequency for teachers who teach math and not English, let's follow a series of steps.

### Step-by-Step Solution:

1. Identify the Joint Frequency (Number of Teachers who Teach Math and Not English):
- From the given table, the number of teachers who teach math and not English is the cell corresponding to "Math" (row) and "Not English" (column).
- This value is 22.

2. Determine the Total Number of Survey Responses:
- The total number of survey responses is given at the bottom right cell of the table.
- This value is 104.

3. Calculate the Joint Relative Frequency:
- The joint relative frequency is calculated as:
[tex]\[ \text{Joint Relative Frequency} = \left( \frac{\text{Joint Frequency}}{\text{Total Survey Responses}} \right) \times 100 \][/tex]
- Plugging in the values:
[tex]\[ \text{Joint Relative Frequency} = \left( \frac{22}{104} \right) \times 100 \][/tex]

4. Convert the Fraction to a Percentage:
- Perform the division and multiplication:
[tex]\[ \left( \frac{22}{104} \right) \times 100 = 21.153846153846153 \][/tex]

5. Round to the Nearest Percent:
- Rounding the result to the nearest whole number gives us:
[tex]\[ 21\% \][/tex]

Thus, the joint relative frequency for teachers who teach math and not English, when rounded to the nearest percent, is 21%.

Other Questions