Question

What is the standard deviation for the data set?

Answer 1

Answer:

The standard deviation is 22.6 to the nearest tenth

Step-by-step explanation:

* Lets study how to find the standard deviation (σ) for data set

- First step find the mean of the data

∵ The mean = the sum of the data ÷ the number of the data

# The sum of the data is

  359 + 320 + 365 + 310 + 349 + 351 + 310 + 314 + 364 = 3042

# The number of the data is 9

∴ The mean = 3042 ÷ 9 = 338

- Second step find the difference between each data and the mean

 and square the difference

# 359 - 338 = 21 ⇒ (21)² = 441

# 320 - 338 = -18 ⇒ (-18)² = 324

# 365 - 338 = 27 ⇒ (27)² = 729

# 310 - 338 = -28 ⇒ (-28)² = 784

# 349 - 338 = 11 ⇒ (11)² = 121

# 351 - 338 = 13 ⇒ (13)² = 169

# 310 - 338 = -28 ⇒ (-28)² = 784

# 314 - 338 = -24 ⇒ (-24)² = 576

# 364 - 338 = 26 ⇒ (26)² = 676

- Third step find the variance (σ²)

# Add all the square difference and divide the sum by the

  number of data

∴ σ² = (441 + 324 + 729 + 784 + 121 + 169 + 784 + 576 + 676) ÷ 9

∴ σ² = 4604 ÷ 9 = 511.5555556

- Fourth step find the standard deviation σ  it is the square root of

 the variance

∴ σ = 22.6 to the nearest tenth

* The standard deviation is 22.6 to the nearest tenth