Answer:
Step-by-step explanation:
Here are the results for the data:
Mean: The mean, or average, of the data can be calculated by summing up all the values and dividing by the number of values:
(11+16+10+30+24+5+6+12+11+45+9+8+3+4+35+31)/16 = 201/16 = 12.5625
So, the mean number of days spent by COVID-19 patients in the ICU is 12.5625 days.
Range: The range of the data is the difference between the maximum and minimum values:
45 - 3 = 42
So, the range of the data is 42 days.
Interquartile Range: The interquartile range (IQR) is a measure of the dispersion of the data that is less sensitive to outliers than the range. To calculate the IQR, we first need to find the median (Q2), first quartile (Q1), and third quartile (Q3) of the data:
Q1 = (6+8)/2 = 7
Q2 = (11+12)/2 = 11.5
Q3 = (24+30)/2 = 27
The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 27 - 7 = 20
Variance and Standard Deviation: Variance is a measure of the dispersion of the data that is used to calculate the standard deviation. The formula for variance is:
Variance = sum of squared deviations from the mean / number of values
First, we need to calculate the deviations from the mean:
11 - 12.5625 = -1.5625
16 - 12.5625 = 3.4375
10 - 12.5625 = -2.5625
...
The sum of the squared deviations from the mean is:
Variance = 596.9375/16 = 37.93359375
The standard deviation is the square root of the variance:
Standard deviation = √Variance = √37.93359375 = 6.15
Coefficient of Variation: The coefficient of variation (CV) is a measure of the relative variability of the data, expressed as a percentage of the mean. The formula for the CV is:
CV = (Standard deviation / mean) * 100
CV = (6.15 / 12.5625) * 100 = 49.03%
Comment on Results:
The mean number of days spent by COVID-19 patients in the ICU at the University of Ghana Medical Centre is 12.5625 days. The range of the data is 42 days, while the interquartile range is 20 days. The variance is 37.93 and the standard deviation is 6.15. The coefficient of variation is 49.03%, which indicates a relatively high degree of variability in the data. These results show that the number of days spent by COVID-19 patients in the ICU at the University of Ghana Medical Centre can vary widely, with some patients spending as few as 3 days and others spending as many as 45 days in the ICU.