Question

rosanne counted the number of fish kept in 7 tanks at the pet store. she counted: 1 fish 5 fish 9 fish 8 fish 9 fish 7 fish 3 fish what was the standard deviation of the numbers of fish? if the answer is a decimal, round it to the nearest tenth. standard deviation (σ): fish

Explanation:

Step1: Calculate the mean ($\mu$)

The data set is \(1, 5, 9, 8, 9, 7, 3\). The number of data points \(n = 7\).
The mean \(\mu=\frac{1 + 5+9 + 8+9 + 7+3}{7}=\frac{42}{7} = 6\).

Step2: Calculate the squared differences from the mean

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

• For \(x = 1\): \((1 - 6)^2=(- 5)^2 = 25\)
• For \(x = 5\): \((5 - 6)^2=(-1)^2 = 1\)
• For \(x = 9\): \((9 - 6)^2=(3)^2 = 9\)
• For \(x = 8\): \((8 - 6)^2=(2)^2 = 4\)
• For \(x = 9\): \((9 - 6)^2=(3)^2 = 9\)
• For \(x = 7\): \((7 - 6)^2=(1)^2 = 1\)
• For \(x = 3\): \((3 - 6)^2=(-3)^2 = 9\)

Step3: Calculate the variance ($\sigma^2$)

Variance is the average of the squared differences.
\(\sigma^2=\frac{25 + 1+9 + 4+9 + 1+9}{7}=\frac{58}{7}\approx8.2857\)

Step4: Calculate the standard deviation ($\sigma$)

Standard deviation is the square root of the variance.
\(\sigma=\sqrt{\frac{58}{7}}\approx\sqrt{8.2857}\approx2.9\) (rounded to the nearest tenth)

Answer:

\(2.9\)