a. Compute the mean and median percentage of hourly employees being laid off at these stores.
Mean
(55 + 56 + 44 + 43 + 44 + 56 + 60 + 62 + 57 + 45 + 36 + 38 + 50 + 69 + 65) / 15 = 52
Median
Since the data set has 15 values, the median is the average of the 7th and 8th values when the data is sorted in ascending order.
55 56 44 43 44 56 60 62 57 45 36 38 50 69 65
43 44 44 45 50 55 56 56 57 60 62 65 69
The median is the average of 50 and 55, which is 52.5.
b. Compute the first and third quartiles.
The first quartile is the median of the lower half of the data set after it has been sorted in ascending order. The third quartile is the median of the upper half of the data set after it has been sorted in ascending order.
43 44 44 45 50 55 56 56 57 60 62 65 69
The first quartile is the median of the first 7 values, which is 44. The third quartile is the median of the last 7 values, which is 60.
c. Compute the range and interquartile range.
The range is the difference between the largest and smallest values in the data set. The interquartile range (IQR) is the difference between the third quartile and the first quartile.
Range = 69 - 43 = 33
IQR = 60 - 44 = 16
d. Compute the variance and standard deviation. Round your answers to four decimal places.
The variance is the average squared deviation from the mean. The standard deviation is the square root of the variance.
Variance = [(55 - 52)^2 + (56 - 52)^2 + (44 - 52)^2 + (43 - 52)^2 + (44 - 52)^2 + (56 - 52)^2 + (60 - 52)^2 + (62 - 52)^2 + (57 - 52)^2 + (45 - 52)^2 + (36 - 52)^2 + (38 - 52)^2 + (50 - 52)^2 + (69 - 52)^2 + (65 - 52)^2] / 15
Variance = 136.3333
Standard deviation = sqrt(136.3333) = 11.69
e. Do the data contain any outliers?
To determine if the data contain any outliers, we can use the following rule of thumb:
Outliers are values that are greater than 1.5 IQRs below the first quartile or 1.5 IQRs above the third quartile.
Lower outlier threshold = Q1 - 1.5 * IQR = 44 - 1.5 * 16 = 16
Upper outlier threshold = Q3 + 1.5 * IQR = 60 + 1.5 * 16 = 88
There are no values in the data set that are less than 16 or greater than 88. Therefore, the data do not contain any outliers.
f. Based on the sample data, does it appear that Walmart is meeting its goal for reducing the number of hourly employees?
The mean percentage of hourly employees being laid off is 52%. This suggests that Walmart is meeting its goal for reducing the number of hourly employees, since the goal is to reduce the number of hourly employees by approximately half.
However, it is important to note that this is just a sample of 15 stores. It is possible that the percentage of hourly employees being laid off is higher or lower at other Sam's Club stores.