Answer:
The variance is 8732.24 and the standard deviation is 93.45
Explanation:
* Lets explain how to find variance and the standard deviation
# Step 1: find the mean of the data set
∵ The mean = the sum of the data ÷ the number of the data
∵ The data set is 3832 , 3779 , 3655 , 3642 , 3579
∵ Their sum = 3832 + 3779 + 3655 + 3642 + 3579 = 18487
∵ They are five numbers
∴ The mean = 18487 ÷ 5 = 3697.4
# Step 2: subtract the mean from each data and square the answer
∴ (3832 - 3697.4)² = 18117.16
∴ (3779 - 3697.4)² = 6658.56
∴ (3655 - 3697.4)² = 1797.76
∴ (3642 - 3697.4)² = 3069.16
∴ (3579 - 3697.4)² = 14018.56
# Step 3: calculate the Variance (σ²) , by adding the square difference,
and divide it by the number of the data
∵ Variance = sum of the square difference ÷ number of the data
∵ The sum = 18117.16 + 6658.56 + 1797.76 + 3069.16 + 14018.56
∴ The sum = 43661.2
∴ σ² = 43661.2 ÷ 5 = 8732.24
# Step 4: the standard deviation (σ) is the square root of variance
∴ The standard deviation = √(8732.24) = 93.446455 ≅ 93.45
* The variance is 8732.24 and the standard deviation is 93.45