e following two grouped frequency distributions represent the times, over a one-week period, that patients had to wait before seeing a doctor in the Accident and Emergency department of two hospitals. Hospital A waiting Times (Minutes) Frequency of Patients Hospital B waiting Times (Minutes) Frequency of Patients 6-10 2 6-10 4 11-15 10 11-15 17 16-20 25 16-20 35 21-25 37 21-25 27 26-30 26 26-30 20 31-35 20 31-35 17 36-40 18 36-40 9 41-45 12 41-45 6 46-50 10 46-50 5 Total 160 Total 140 a) Determine the mean and standard deviation of waiting times for each hospital; b) Determine the coefficient of variation for each hospital’s waiting times; c) Determine the coefficient of skewness for each hospital’s waiting times; d) With reference to parts (a), (b) and (c) discuss the differences in waiting times between the two hospitals.
e following two grouped frequency distributions represent the times, over a one-week period, that patients had to wait before seeing a doctor in the Accident and Emergency department of two hospitals. Hospital A waiting Times (Minutes) Frequency of Patients Hospital B waiting Times (Minutes) Frequency of Patients 6-10 2 6-10 4 11-15 10 11-15 17 16-20 25 16-20 35 21-25 37 21-25 27 26-30 26 26-30 20 31-35 20 31-35 17 36-40 18 36-40 9 41-45 12 41-45 6 46-50 10 46-50 5 Total 160 Total 140 a) Determine the mean and standard deviation of waiting times for each hospital; b) Determine the coefficient of variation for each hospital’s waiting times; c) Determine the coefficient of skewness for each hospital’s waiting times; d) With reference to parts (a), (b) and (c) discuss the differences in waiting times between the two hospitals.
The following two grouped frequency distributions represent the times, over a one-week period, that patients had to wait before seeing a doctor in the Accident and Emergency department of two hospitals.
Hospital A waiting Times (Minutes)
Frequency of Patients
Hospital B waiting Times (Minutes)
Frequency of Patients
6-10
2
6-10
4
11-15
10
11-15
17
16-20
25
16-20
35
21-25
37
21-25
27
26-30
26
26-30
20
31-35
20
31-35
17
36-40
18
36-40
9
41-45
12
41-45
6
46-50
10
46-50
5
Total
160
Total
140
a) Determine the meanand standard deviation of waiting times for each hospital;
b) Determine the coefficient of variation for each hospital’s waiting times;
c) Determine the coefficient of skewness for each hospital’s waiting times;
d) With reference to parts (a), (b) and (c) discuss the differences in waiting times between the two hospitals.
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 + ...
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