To calculate the mean number of sit-ups done in a minute, we need to follow these steps:
1. Identify the data provided:
- Sit-ups in a minute and their respective frequencies.
2. Calculate the total number of sit-ups performed:
- This is the sum of the product of sit-ups and their respective frequencies.
3. Calculate the total frequency:
- This is the sum of all the frequencies.
4. Calculate the mean number of sit-ups:
- Divide the total number of sit-ups by the total frequency.
### Step-by-Step Solution:
1. Given Data:
| Sit-Ups in a minute | Frequency |
|---------------------|-----------|
| 15 | 13 |
| 16 | 5 |
| 17 | 13 |
| 18 | 17 |
| 19 | 22 |
| 20 | 22 |
| 21 | 22 |
| 22 | 17 |
2. Calculate the total number of sit-ups performed:
[tex]\[
\text{Total sit-ups} = (15 \times 13) + (16 \times 5) + (17 \times 13) + (18 \times 17) + (19 \times 22) + (20 \times 22) + (21 \times 22) + (22 \times 17)
\][/tex]
Substituting the values:
[tex]\[
\text{Total sit-ups} = 195 + 80 + 221 + 306 + 418 + 440 + 462 + 374 = 2496
\][/tex]
3. Calculate the total frequency:
[tex]\[
\text{Total frequency} = 13 + 5 + 13 + 17 + 22 + 22 + 22 + 17 = 131
\][/tex]
4. Calculate the mean number of sit-ups:
[tex]\[
\text{Mean sit-ups} = \frac{\text{Total sit-ups}}{\text{Total frequency}} = \frac{2496}{131} \approx 19.053435114503817
\][/tex]
Therefore, the mean number of sit-ups done in a minute is approximately [tex]\( 19.1 \)[/tex].
### Conclusion:
The correct answer is B. 19.1.
