1. Collected data shows that about 220,000 high schoolers took the AP in 2020. The FRQ section of the exam consisted of five problems. Each FRQ is scored on a o to 4 scale (with 4 being the best). For a certain problem, a random sample of 35 submissions produced a mean score of i =1.627 and a standard deviation of 3, = 1.320. A. Find the standard error of the mean and interpret it. B. Construct a 99% confidence interval to estimate the true mean score on this question and interpret it.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...