The speed of cars driving past Johnson City High School, on 666 Reynolds Rd, were recorded over one school year. The speed limit on that part of Reynolds Rd is 20 mph. The mean of the speed readings was 24.19 mph, with a standard deviation of 3.56 mph. i) How many standard deviations from the mean would a car going under the speed limit be? ii) Which would be more unusual, a car travelling 34 mph or one going 10 mph? Explain. iii) The police handed out a large number of tickets to speeders. The mean number of mph over the speed limit for these speeders was 7, with a standard deviation of 2.3 mph, a maximum of 12 mph and an IQR 3.1 mph. Local law prescribes fines of $100, plus $10 per mile per hour over the 20 mph speed limit. For example, a driver convicted of going 25 mph would be fined 100+10 (5) = $150. Find the mean, maximum, standard deviation and IQR of all potential fines.

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 + ...