the graph shows a distribution of data. what is the variance of the data? 0.0625 0.25 0.5 1.5
the graph shows a distribution of data. what is the variance of the data? 0.0625 0.25 0.5 1.5
Answer
Explanation:
Step1: Assume normal - distribution properties
For a normal distribution, if we assume the data is symmetric and we know that in a normal distribution, about 68% of the data lies within 1 standard - deviation ($\sigma$) of the mean. Looking at the graph, if we assume the mean is around 4 and the range within 1 - standard deviation is from 3.5 to 4.5. Then $\sigma=4.5 - 4=0.5$.
Step2: Recall the variance formula
The variance ($\sigma^{2}$) is the square of the standard - deviation. Since $\sigma = 0.5$, then $\sigma^{2}=(0.5)^{2}=0.25$.
Answer:
0.25