Using the data in the table, calculate the mean, range, variance, and standard deviation, and then answer questions e and f. Round the variance and standard deviation to one decimal place.
a. Mean
b. Range
c. Variance
d. Standard deviation
e. What value is affecting the mean and SD of this distribution?
f. Does the mean adequately represent this distribution? If not, what would be a better measure of central tendency for this data set?
Patient Length of Stay LOS-Mean(5) (LOS –mean)2
(X-X)
1 1
2 3
3 5
4 3
5 2
6 29
7 3
8 4
9 2
10 1
11 2
To calculate the mean, range, variance, and standard deviation, you need to follow these steps:
a. Mean:
To calculate the mean, sum up all the values and divide the sum by the total number of values.
Mean = (1 + 3 + 5 + 3 + 2 + 29 + 3 + 4 + 2 + 1 + 2) / 11
b. Range:
To calculate the range, subtract the smallest value from the largest value.
Range = Largest Value - Smallest Value
c. Variance:
First, calculate the squared difference of each value from the mean:
(X - X)^2 = (1 - Mean)^2, (3 - Mean)^2, (5 - Mean)^2, ...
Next, calculate the mean of these squared differences: Sum of all (X - X)^2 / Total Number of Values
Variance = Sum of (X - X)^2 / Number of Values
d. Standard Deviation:
The standard deviation is the square root of the variance.
Standard Deviation = Square root of Variance
e. To identify the value affecting the mean and standard deviation, you need to compare each value with the other values in the dataset. Look for any outliers or extremely large or small values that might skew the results.
f. Whether the mean adequately represents the distribution depends on the data and your goals. If the distribution is skewed or has extreme outliers, the mean might not provide an accurate representation of the central tendency. In such cases, a better measure of central tendency could be the median, which represents the middle value in a dataset. Additionally, you might want to consider the mode, which represents the most frequently occurring value, if applicable.