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The Wall Street Journal reported that Walmart Stores Inc. is planning to lay off 2,300 employees at its Sam's Club warehouse unit. Approximately half of the layoffs will be hourly employees (The Wall Street Journal, January 25-26, 2014). Suppose the following data represent the percentage of hourly employees laid off for 15 Sam's Club stores.

55 56 44 43 44 56 60 62 57 45 36 38 50 69 65
a. Compute the mean and median percentage of hourly employees being laid off at these stores.

Mean
52
Median
55
b. Compute the first and third quartiles.

First quartile
44
Third quartile
60
c. Compute the range and interquartile range.

Range
33
Interquartile range
16
d. Compute the variance and standard deviation. Round your answers to four decimal places.

Variance
Standard deviation
e. Do the data contain any outliers?

- Select your answer -

f. Based on the sample data, does it appear that Walmart is meeting its goal for reducing the number of hourly employees?

- Select your answer -

1 Answer

5 votes

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.

User Kylaaa
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