Question

The Wall Street Journal reported that Walmart Stores Inc. is planning to lay off 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 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 Median
b. Compute the first and third quartiles. First quartile Third quartile
c. Compute the range and interquartile range. Range Interquartile range
d. Compute the variance and standard deviation. Round your answers to four decimal places. Variance Standard deviation
e. Do the data contain any outliers

Answer 1

Answer:

a) $\bar X = 52$

$Median = 55$

b) $Q_1= \frac{44+44}{2}=44$

$Q_3= \frac{57+60}{2}=58.5$

c) $Range = Max -Min = 69-36=33$

d) $s^2 =100.1429$

$s= \sqrt{100.143}=10.0071$

e) $Lower = Q_1 -1.5 IQR = 44-1.5(58.5-44) = 22.25$

$Upper = Q_1 +1.5 IQR = 44+1.5(58.5-44) = 65.75$

A possible outlier would be the value of 69 since its above the upper limti for the boxplot.

Step-by-step explanation:

For this case we have the following dataset:

55 56 44 43 44 56 60 62 57 45 36 38 50 69 65

A total of 15 observations

Part a

We calculate the mean with the following formula:

$\bar X = \frac{\sum_{i=1}^{15} X_i}{15}$

And for this case we got $\bar X = 52$

For the median we ust need to order the data on increasing way like this:

36, 38,43,44,44,45,50,55,56,56,57,60,62,65,69

Since the number of observations is an odd number the median would be on the 8 position from the dataset ordered on this case:

$Median = 55$

Part b

In order to calculate the Q1 we need to select the following data:

36, 38,43,44,44,45,50,55

And the Q1 would be the average between the 4 and 5 positions like this:

$Q_1= \frac{44+44}{2}=44$

And for the Q3 we select these values:

55,56,56,57,60,62,65,69

And the Q3 would be the average between the 4 and 5 positions like this:

$Q_3= \frac{57+60}{2}=58.5$

Part c

The Range is defined as:

$Range = Max -Min = 69-36=33$

Part d

In order to calculate the sample variance we can use the following formula:

$s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

And if we replace we got:

$s^2 =100.1429$

And the deviation is just the square root of the variance:

$s= \sqrt{100.143}=10.0071$

Part e

For this case we need to find the lower and upper limits for the boxplot given by:

$Lower = Q_1 -1.5 IQR = 44-1.5(58.5-44) = 22.25$

$Upper = Q_1 +1.5 IQR = 44+1.5(58.5-44) = 65.75$

A possible outlier would be the value of 69 since its above the upper limti for the boxplot.