A Sewing Supply Company Has a Database of Tens of Thousands

question 131

Essay

A sewing supply company has a database of tens of thousands of products that they sell in their stores.One of the variables in the database,Thread_Colour,contains the names of the colors of the various spools of thread that are sold.The most commonly sold are white,black,and brown,but there are also magenta,azure,sea foam green,and nutmeg,to name a few others.In all there are more than 500 different colours,each with a corresponding numeric code.Here are a few of them: $$\begin{array} { | l | l | } \hline \text { Code } & \text { Colour } \\\hline 000 & \text { white } \\\hline 001 & \text { black } \\\hline 002 & \text { prown } \\\hline 003 & \text { yellow } \\\hline 004 & \text { plue } \\\hline 005 & \text { red } \\\hline 009 & \text { violet } \\\hline 010 & \text { magenta } \\ \hline 127 & \text { sea foam } \\& \text { green } \\\hline 128 & \text { hutmeg } \\\hline 134 & \text { turquoise } \\\hline 159 & \text { evergreen } \\\hline 687 & \text { midnight blue } \\\hline 508 & \text { teal } \\\hline\end{array}$$ An intern who was asked to analyze the company's thread sales presented these summary statistics for the variable Thread_Colour: $$\begin{array} { | l | l | } \hline \text { Mean } & 35.89 \\\hline \text { StdDev } & 784.92 \\\hline \text { Median } & 2 \\\hline \mathrm { IQR } & 3 \\\hline \mathrm { n } & 87602 \\\hline\end{array}$$ a)What does the mean of 35.89 mean?
b)What are the typical reasons that cause measures of centre and spread to be as different as those in this table?
c)Is that why these are so different?

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Definitions:

Direct Labor Efficiency Variance

The difference between the budgeted amount of direct labor required to produce an output and the actual direct labor used.

Favorable

A term used in budgeting and finance to indicate results that are better than expected, such as lower costs or higher revenues.

Unfavorable

A term used to describe outcomes or variances that negatively impact financial performance or expectations.

Unfavorable Variances

Occurrences when actual costs exceed budgeted or expected costs, indicating a potential need for management action to address inefficiencies.