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URGENT!! 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)

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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

User Ken Aspeslagh
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