Question
Thabo and John play for varsity cricket team, here are their scores of their last 10 innings:
Thabo: 13 127 64 37 83 27 0 103 12 48 and
John: 61 53 40 48 62 32 40 69 43 53
Calculate John's standard deviation. (3)
SELECT THE CORRECT ANSWER
12,1
11,647
42,217
None of the given answers
Thabo: 13 127 64 37 83 27 0 103 12 48 and
John: 61 53 40 48 62 32 40 69 43 53
Calculate John's standard deviation. (3)
SELECT THE CORRECT ANSWER
12,1
11,647
42,217
None of the given answers
Answers
Answered by
GPT-4o mini
To calculate John's standard deviation, we will follow these steps:
1. Calculate the mean (average) of John's scores.
2. Find the squared differences from the mean for each score.
3. Calculate the variance by averaging these squared differences.
4. Take the square root of the variance to find the standard deviation.
**Step 1: Calculate the mean**
John's scores: 61, 53, 40, 48, 62, 32, 40, 69, 43, 53
Mean (\( \mu \)) = (Sum of scores) / (Number of scores)
Sum of scores = 61 + 53 + 40 + 48 + 62 + 32 + 40 + 69 + 43 + 53 = 459
Number of scores = 10
Mean (\( \mu \)) = 459 / 10 = 45.9
**Step 2: Calculate the squared differences from the mean**
- (61 - 45.9)² = 15.1² = 228.01
- (53 - 45.9)² = 7.1² = 50.41
- (40 - 45.9)² = -5.9² = 34.81
- (48 - 45.9)² = 2.1² = 4.41
- (62 - 45.9)² = 16.1² = 259.21
- (32 - 45.9)² = -13.9² = 193.21
- (40 - 45.9)² = -5.9² = 34.81
- (69 - 45.9)² = 23.1² = 533.61
- (43 - 45.9)² = -2.9² = 8.41
- (53 - 45.9)² = 7.1² = 50.41
**Step 3: Calculate the variance**
Sum of squared differences = 228.01 + 50.41 + 34.81 + 4.41 + 259.21 + 193.21 + 34.81 + 533.61 + 8.41 + 50.41 = 1061.6
Variance (\( \sigma^2 \)) = (Sum of squared differences) / (Number of scores)
Variance = 1061.6 / 10 = 106.16
**Step 4: Calculate the standard deviation**
Standard deviation (\( \sigma \)) = √Variance = √106.16 ≈ 10.3 (rounded to one decimal place)
Since we are looking for a solution from the answers given, it seems like standard deviation as calculated above does not match any of the options.
Therefore, the correct answer is:
**None of the given answers.**
1. Calculate the mean (average) of John's scores.
2. Find the squared differences from the mean for each score.
3. Calculate the variance by averaging these squared differences.
4. Take the square root of the variance to find the standard deviation.
**Step 1: Calculate the mean**
John's scores: 61, 53, 40, 48, 62, 32, 40, 69, 43, 53
Mean (\( \mu \)) = (Sum of scores) / (Number of scores)
Sum of scores = 61 + 53 + 40 + 48 + 62 + 32 + 40 + 69 + 43 + 53 = 459
Number of scores = 10
Mean (\( \mu \)) = 459 / 10 = 45.9
**Step 2: Calculate the squared differences from the mean**
- (61 - 45.9)² = 15.1² = 228.01
- (53 - 45.9)² = 7.1² = 50.41
- (40 - 45.9)² = -5.9² = 34.81
- (48 - 45.9)² = 2.1² = 4.41
- (62 - 45.9)² = 16.1² = 259.21
- (32 - 45.9)² = -13.9² = 193.21
- (40 - 45.9)² = -5.9² = 34.81
- (69 - 45.9)² = 23.1² = 533.61
- (43 - 45.9)² = -2.9² = 8.41
- (53 - 45.9)² = 7.1² = 50.41
**Step 3: Calculate the variance**
Sum of squared differences = 228.01 + 50.41 + 34.81 + 4.41 + 259.21 + 193.21 + 34.81 + 533.61 + 8.41 + 50.41 = 1061.6
Variance (\( \sigma^2 \)) = (Sum of squared differences) / (Number of scores)
Variance = 1061.6 / 10 = 106.16
**Step 4: Calculate the standard deviation**
Standard deviation (\( \sigma \)) = √Variance = √106.16 ≈ 10.3 (rounded to one decimal place)
Since we are looking for a solution from the answers given, it seems like standard deviation as calculated above does not match any of the options.
Therefore, the correct answer is:
**None of the given answers.**