Question
Susie took 5
tests in her Algebra class. She scored an 91,75,79,85,
and 87
. What is the standard deviation of her grades in these test?
If necessary, round to the nearest hundredth.
A. 32.64
B.5.21
C. 5.71
D. 27.14
Best answer
tests in her Algebra class. She scored an 91,75,79,85,
and 87
. What is the standard deviation of her grades in these test?
If necessary, round to the nearest hundredth.
A. 32.64
B.5.21
C. 5.71
D. 27.14
Best answer
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the standard deviation of Susie's test scores, we can follow these steps:
1. **Calculate the mean (average)** of the scores.
2. **Calculate the variance** by finding the squared differences from the mean, averaging those, and then taking the square root to obtain the standard deviation.
**Step 1: Calculate the mean**
The scores are: 91, 75, 79, 85, and 87.
Mean = (91 + 75 + 79 + 85 + 87) / 5
Mean = (417) / 5 = 83.4
**Step 2: Calculate the squared differences from the mean**
- (91 - 83.4)² = (7.6)² = 57.76
- (75 - 83.4)² = (-8.4)² = 70.56
- (79 - 83.4)² = (-4.4)² = 19.36
- (85 - 83.4)² = (1.6)² = 2.56
- (87 - 83.4)² = (3.6)² = 12.96
**Step 3: Calculate the variance**
Variance = (Sum of squared differences) / (Number of scores)
Variance = (57.76 + 70.56 + 19.36 + 2.56 + 12.96) / 5
Variance = (163.2) / 5 = 32.64
**Step 4: Calculate the standard deviation**
Standard deviation = √Variance
Standard deviation = √32.64 ≈ 5.71
So the standard deviation of Susie's grades is approximately **5.71**.
The best answer is **C. 5.71**.
1. **Calculate the mean (average)** of the scores.
2. **Calculate the variance** by finding the squared differences from the mean, averaging those, and then taking the square root to obtain the standard deviation.
**Step 1: Calculate the mean**
The scores are: 91, 75, 79, 85, and 87.
Mean = (91 + 75 + 79 + 85 + 87) / 5
Mean = (417) / 5 = 83.4
**Step 2: Calculate the squared differences from the mean**
- (91 - 83.4)² = (7.6)² = 57.76
- (75 - 83.4)² = (-8.4)² = 70.56
- (79 - 83.4)² = (-4.4)² = 19.36
- (85 - 83.4)² = (1.6)² = 2.56
- (87 - 83.4)² = (3.6)² = 12.96
**Step 3: Calculate the variance**
Variance = (Sum of squared differences) / (Number of scores)
Variance = (57.76 + 70.56 + 19.36 + 2.56 + 12.96) / 5
Variance = (163.2) / 5 = 32.64
**Step 4: Calculate the standard deviation**
Standard deviation = √Variance
Standard deviation = √32.64 ≈ 5.71
So the standard deviation of Susie's grades is approximately **5.71**.
The best answer is **C. 5.71**.
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