Final answer:
The student is looking to calculate the variance and standard deviation of recorded temperatures. The variance is roughly 0.513 while the standard deviation is approximately 0.716. Additionally, two standard deviations above the mean temperature is about 99.832 degrees Fahrenheit.
Step-by-step explanation:
The student is tasked with finding the variance and standard deviation of recorded high temperatures, which are key statistical measures that indicate how much a set of data is spread out. The variance (s²) is calculated by summing the squared deviations of each data point from the mean, then dividing by the total number of observations minus one. The standard deviation (s) is the square root of the variance and provides a measure of dispersion in the units of the original data.
With a provided sample variance of 9.7375 from 20 data values, we calculate the variance by dividing 9.7375 by (20 - 1), which results in a sample variance of approximately 0.513. To find the sample standard deviation, we take the square root of the variance, giving us approximately 0.716. This value quantifies the average distance of data points from the mean.
To find the value that is two standard deviations above the mean, we simply add twice the standard deviation to the sample mean: 98.4 + (2 × 0.716) = 98.4 + 1.432 = approximately 99.832 degrees Fahrenheit.