The table below shows the LOS for a sample of 11 discharged patients. 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-x̅) (x-x̅)2
1 1
2 3
3 5
4 3
5 2
6 29
7 3
8 4
9 2
10 1
11 2
I honestly don't understand how to do this. If someone can help me out and guide me in the right direction I would appreciate it. I need to get this right on a test.
It didn't come out right, the numbers 1,3,5,3,2, 29,3, 4, 2, 1, 2 are supposed to be under the column of length of stay. Columns Los-mean (5) and LOS-Mean)2 are intentionally left empty. And the x-x) and (x-x)2 signs are under the LOS mean columns.
I need help, someone please help me with this.
a.
mean = (1+3+5+3+2+29+3+4+2+1+2)/11 =55/11= 5
(1-5) =
x (x-x̅) (x-x̅)^2
1 -4 16
3 -2 4
5 0 0
3 -2 4
2 -3 9
29 24 576
3 -2 4
4 -1 1
2 -3 9
1 -4 16
2 -3 9
b.
Range= highest value - lowest value
Range =29-1 = 28
c. variance = (x-x̅)^2 = 648
648/(11-) = 64.8
d. standard deviation = Sqrt(variance) = sqrt(64.8) =8.04984
To calculate the mean, range, variance, and standard deviation for the given data set, follow these steps:
a. Mean:
1. Add up all the values in the "Length of Stay" column: 1 + 3 + 5 + 3 + 2 + 29 + 3 + 4 + 2 + 1 + 2 = 55.
2. Divide the sum by the number of values (11): 55 ÷ 11 = 5.
Therefore, the mean is 5.
b. Range:
1. Find the maximum value in the "Length of Stay" column: 29.
2. Find the minimum value in the "Length of Stay" column: 1.
3. Calculate the range by subtracting the minimum value from the maximum value: 29 - 1 = 28.
Therefore, the range is 28.
c. Variance:
1. Subtract the mean from each value in the "Length of Stay" column (x - x̅) and record the results in the "LOS-Mean" column: -4, -2, 0, -2, -3, 24, -2, -1, -3, -4, -3.
2. Square each value in the "LOS-Mean" column and record the results in the "(LOS-Mean)2" column: 16, 4, 0, 4, 9, 576, 4, 1, 9, 16, 9.
3. Add up all the values in the "(LOS-Mean)2" column: 648.
4. Divide the sum by the number of values (11): 648 ÷ 11 = 58.9 (rounded to one decimal place).
Therefore, the variance is 58.9.
d. Standard deviation:
1. Take the square root of the variance calculated in step c: √58.9 ≈ 7.7 (rounded to one decimal place).
Therefore, the standard deviation is 7.7.
e. The high value of 29 is affecting both the mean and standard deviation of this distribution. Since it is an outlier, it deviates significantly from the other values, leading to a higher mean and standard deviation.
f. No, the mean does not adequately represent this distribution because it is heavily influenced by the outlier value of 29. A better measure of central tendency for this data set would be the median, as it is less affected by outliers.
To calculate the mean, range, variance, and standard deviation for the given data, follow these steps:
a. Mean:
To calculate the mean, add up all the values and divide the sum by the number of values (11 in this case).
Mean = (1 + 3 + 5 + 3 + 2 + 29 + 3 + 4 + 2 + 1 + 2) / 11
b. Range:
To calculate the range, find the difference between the maximum and minimum values in the dataset.
Range = Maximum value - Minimum value
c. Variance:
To calculate the variance, follow these steps:
1. Subtract the mean from each value to get the deviation from the mean (LOS-Mean).
2. Square each deviation (LOS-Mean) and add up all the squared deviations.
3. Divide the sum of squared deviations by the number of values (11) to get the variance.
Variance = Sum of ((LOS-Mean)2) / Number of values
d. Standard deviation:
To calculate the standard deviation, take the square root of the variance.
Standard deviation = Square root of variance
Once you have calculated these values, proceed to answer questions e and f.
e. What value is affecting the mean and SD of this distribution?
To determine the value affecting the mean and standard deviation, look for any outliers or extreme values in the dataset. These values can significantly influence the mean and standard deviation, pulling them away from the typical values.
f. Does the mean adequately represent this distribution? If not, what would be a better measure of central tendency for this data set?
To determine if the mean adequately represents the distribution, consider the presence of outliers or extreme values. If there are significant outliers, the mean may not provide an accurate representation of the central tendency. In such cases, using the median (middle value when the data is sorted in ascending order) as a measure of central tendency might be more appropriate.
By following these steps, you should be able to calculate the mean, range, variance, and standard deviation for the given dataset and answer questions e and f.