Yellowstone Park Medical Services (YPMS) provides emergency health care for park visitors. Such health care includes treatment for everything from indigestion and sunburn to more serious injuries. A recent issue of Yellowstone Today (National Park Service Publication) indicated that the average number of visitors treated each day by YPMS was 21.7. The estimated standard deviation was 4.2 (summer data). The distribution of numbers treated is approximately mound-shaped and symmetric. (a) For a 10-day summer period, the following data show the number of visitors treated each day by YPMS. Day 1 2 3 4 5 6 7 8 9 10 Number treated 25 19 17 15 20 24 30 19 16 23Make a control chart for the daily number of visitors treated by YPMS, and plot the data on the control chart. (Be sure to include the horizontal lines on the control chart. Recall that the mean line is solid and the control limit lines are dashed.)   For another 10-day summer period, the following data were obtained. Day 1 2 3 4 5 6 7 8 9 10 Number treated 20 15 12 21 24 28 32 36 35 37Make a control chart, and plot the data on the chart. (Be sure to include the horizontal lines on the control chart. Recall that the mean line is solid and the control limit lines are dashed.)

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 + ...