The passing yards for the top 5 quarterbacks in the country are 3,832, 3,779, 3,655, 3,642, and 3,579. find the variance and standard deviation. round to the nearest hundredth.
(explain work)

The variance is 8732.24 and the standard deviation is 93.45

Step-by-step 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

the correct answer is 1.7