Question

the dot - plot below shows the lengths of 10 new afrobeat songs. the mean of the data set is 4. what is the standard deviation of the data set, rounded to the nearest hundredth? standard deviation = √(sum of squared distances from mean / total number of data points) type the number in the box. round your answer to the nearest hundredth.

Explanation:

Step1: Identify data points

The data points from the dot - plot are: 2.5, 3, 3, 4, 4, 4, 4.5, 5, 5, 5. The mean of the data set is given as 4.

Step2: Calculate squared distances

For 2.5: $(2.5 - 4)^2=( - 1.5)^2 = 2.25$.
For 3: $(3 - 4)^2=( - 1)^2 = 1$ (and there are 2 values of 3, so total contribution is $2\times1 = 2$).
For 4: $(4 - 4)^2=0$ (and there are 3 values of 4, so total contribution is $3\times0 = 0$).
For 4.5: $(4.5 - 4)^2=(0.5)^2 = 0.25$.
For 5: $(5 - 4)^2=1$ (and there are 3 values of 5, so total contribution is $3\times1 = 3$).
The sum of squared distances is $2.25+2 + 0+0.25+3=7.5$.

Step3: Calculate standard deviation

The formula for standard deviation is $\sigma=\sqrt{\frac{\text{sum of squared distances}}{\text{total number of data points}}}$. Here, the total number of data points is 10.
So, $\sigma=\sqrt{\frac{7.5}{10}}=\sqrt{0.75}\approx0.87$.

Answer:

$0.87$