SOLUTION: For this freqeuncy distribution find the:
A. Sample mean: (round to two decimal places)
B. Sample Standard Deviation (round to two decimal places)
X Frequency
1
Algebra ->
Probability-and-statistics
-> SOLUTION: For this freqeuncy distribution find the:
A. Sample mean: (round to two decimal places)
B. Sample Standard Deviation (round to two decimal places)
X Frequency
1
Log On
Question 1179844: For this freqeuncy distribution find the:
A. Sample mean: (round to two decimal places)
B. Sample Standard Deviation (round to two decimal places)
X Frequency
1 3
2 7
4 10
6 8
7 4 Answer by CPhill(1959) (Show Source):
You can put this solution on YOUR website! Here's how to calculate the sample mean and sample standard deviation for the given frequency distribution:
**A. Sample Mean (x̄):**
1. **Calculate the sum of (x * frequency):**
* (1 * 3) + (2 * 7) + (4 * 10) + (6 * 8) + (7 * 4) = 3 + 14 + 40 + 48 + 28 = 133
2. **Calculate the total frequency (n):**
* 3 + 7 + 10 + 8 + 4 = 32
3. **Calculate the sample mean:**
* x̄ = (sum of (x * frequency)) / n
* x̄ = 133 / 32 ≈ 4.16
**B. Sample Standard Deviation (s):**
1. **Calculate (x - x̄)² for each x:**
* (1 - 4.16)² ≈ 9.99
* (2 - 4.16)² ≈ 4.67
* (4 - 4.16)² ≈ 0.03
* (6 - 4.16)² ≈ 3.39
* (7 - 4.16)² ≈ 8.07
2. **Multiply each (x - x̄)² by its frequency:**
* 9.99 * 3 ≈ 29.97
* 4.67 * 7 ≈ 32.69
* 0.03 * 10 ≈ 0.3
* 3.39 * 8 ≈ 27.12
* 8.07 * 4 ≈ 32.28
3. **Calculate the sum of the results from step 2:**
* 29.97 + 32.69 + 0.3 + 27.12 + 32.28 = 122.36
4. **Divide by (n - 1):**
* 122.36 / (32 - 1) = 122.36 / 31 ≈ 3.947
5. **Take the square root:**
* s = √3.947 ≈ 1.99
**Answers:**
A. Sample mean: 4.16
B. Sample standard deviation: 1.99
