Question

tony took a magazine quiz with 5 friends. they each scored: 1 point 3 points 2 points 9 points 1 point what was the standard deviation of the scores? if the answer is a decimal, round it to the nearest tenth. standard deviation (σ): points

Explanation:

Step1: Calculate the mean (μ)

First, find the sum of the scores. The scores are 1, 3, 2, 9, 1.
Sum = \(1 + 3 + 2 + 9 + 1 = 16\)
There are 5 scores, so the mean \(\mu=\frac{16}{5}=3.2\)

Step2: Find the squared differences from the mean

For each score \(x\), calculate \((x - \mu)^2\):

• For \(x = 1\): \((1 - 3.2)^2 = (-2.2)^2 = 4.84\)
• For \(x = 3\): \((3 - 3.2)^2 = (-0.2)^2 = 0.04\)
• For \(x = 2\): \((2 - 3.2)^2 = (-1.2)^2 = 1.44\)
• For \(x = 9\): \((9 - 3.2)^2 = (5.8)^2 = 33.64\)
• For \(x = 1\): \((1 - 3.2)^2 = (-2.2)^2 = 4.84\)

Step3: Calculate the variance (σ²)

Variance is the average of the squared differences.
Sum of squared differences = \(4.84 + 0.04 + 1.44 + 33.64 + 4.84 = 44.8\)
Variance \(\sigma^2=\frac{44.8}{5}=8.96\)

Step4: Calculate the standard deviation (σ)

Standard deviation is the square root of the variance.
\(\sigma=\sqrt{8.96}\approx 3.0\) (rounded to the nearest tenth)

Answer:

3.0