Question
♡
Calculate the standard deviation of the data set. Round to the nearest tenth.
(20, 35, 41, 48, 79, 83, 83, 97, 120}
(1 point)
32.9
31.0
29.8
Ο 79.0
Calculate the standard deviation of the data set. Round to the nearest tenth.
(20, 35, 41, 48, 79, 83, 83, 97, 120}
(1 point)
32.9
31.0
29.8
Ο 79.0
Answers
GPT-4o mini
To calculate the standard deviation of the given data set \( (20, 35, 41, 48, 79, 83, 83, 97, 120) \), follow these steps:
1. **Find the mean (average)**:
\[
\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}} = \frac{20 + 35 + 41 + 48 + 79 + 83 + 83 + 97 + 120}{9}
\]
\[
= \frac{506}{9} \approx 56.22
\]
2. **Calculate the variance**:
- Subtract the mean from each data point, square the result, and then average those squared differences.
\[
\text{Variance} = \frac{(20 - 56.22)^2 + (35 - 56.22)^2 + (41 - 56.22)^2 + (48 - 56.22)^2 + (79 - 56.22)^2 + (83 - 56.22)^2 + (83 - 56.22)^2 + (97 - 56.22)^2 + (120 - 56.22)^2}{9}
\]
\[
= \frac{( -36.22)^2 + ( -21.22)^2 + ( -15.22)^2 + ( -8.22)^2 + (22.78)^2 + (26.78)^2 + (26.78)^2 + (40.78)^2 + (63.78)^2}{9}
\]
\[
= \frac{1315.0884 + 451.0884 + 232.1284 + 67.0884 + 518.3684 + 711.0884 + 711.0884 + 1663.7284 + 4063.0884}{9}
\]
\[
= \frac{11281.392}{9} \approx 1253.6
\]
3. **Calculate the standard deviation**:
- The standard deviation is the square root of the variance.
\[
\text{Standard Deviation} = \sqrt{1253.6} \approx 35.4
\]
Now rounding this to the nearest tenth, we find that the standard deviation is approximately **35.4**.
As such, if we were to choose from the given options:
- **32.9**
- **31.0**
- **29.8**
- **79.0**
None of the provided options is correct, based on our calculated result of 35.4. Please check if all information was entered correctly or if there are additional options, as there seems to be a discrepancy.
1. **Find the mean (average)**:
\[
\text{Mean} = \frac{\text{Sum of all data points}}{\text{Number of data points}} = \frac{20 + 35 + 41 + 48 + 79 + 83 + 83 + 97 + 120}{9}
\]
\[
= \frac{506}{9} \approx 56.22
\]
2. **Calculate the variance**:
- Subtract the mean from each data point, square the result, and then average those squared differences.
\[
\text{Variance} = \frac{(20 - 56.22)^2 + (35 - 56.22)^2 + (41 - 56.22)^2 + (48 - 56.22)^2 + (79 - 56.22)^2 + (83 - 56.22)^2 + (83 - 56.22)^2 + (97 - 56.22)^2 + (120 - 56.22)^2}{9}
\]
\[
= \frac{( -36.22)^2 + ( -21.22)^2 + ( -15.22)^2 + ( -8.22)^2 + (22.78)^2 + (26.78)^2 + (26.78)^2 + (40.78)^2 + (63.78)^2}{9}
\]
\[
= \frac{1315.0884 + 451.0884 + 232.1284 + 67.0884 + 518.3684 + 711.0884 + 711.0884 + 1663.7284 + 4063.0884}{9}
\]
\[
= \frac{11281.392}{9} \approx 1253.6
\]
3. **Calculate the standard deviation**:
- The standard deviation is the square root of the variance.
\[
\text{Standard Deviation} = \sqrt{1253.6} \approx 35.4
\]
Now rounding this to the nearest tenth, we find that the standard deviation is approximately **35.4**.
As such, if we were to choose from the given options:
- **32.9**
- **31.0**
- **29.8**
- **79.0**
None of the provided options is correct, based on our calculated result of 35.4. Please check if all information was entered correctly or if there are additional options, as there seems to be a discrepancy.