Question

the graph represents the distribution of the number of questions answered correctly on a 50 - question math test. what is the standard deviation of the data? 4 8 12 24 math test scores 24 28 32 36 40 44 48 x

Explanation:

Step1: Recall property of normal - distribution

In a normal - distribution, approximately 68% of the data lies within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. If we assume the mean is around 36 (the peak of the bell - shaped curve) and we consider the range within 1 standard deviation on either side of the mean. A common way to estimate the standard deviation from a normal - distribution graph is to look at the spread. If we consider the fact that the data seems to be symmetric around the mean and we assume that the interval from 32 to 40 (a range of 8) represents approximately 2 standard deviations (since about 68% of the data is within 1 standard deviation on either side of the mean in a normal distribution).

Step2: Calculate standard deviation

If the range of values within 2 standard deviations is 8, then the standard deviation $\sigma=\frac{8}{2}=4$.

Answer:

4