The Weights of Five Players on a Football Team Are

question 91

Essay

The weights of five players on a football team are shown below.

$$\begin{array} { r | r r r r r } \text { Player } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\\hline \text { Weight (lb) } & 290 & 320 & 250 & 255 & 220\end{array}$$
Consider these five players to be a population. Construct a table which shows all of the possible samples of size two which can be selected without replacement. For each of the possible samples, list the players in the sample, their weights, and the sample mean $\bar { x }$ of the weights. The first line of the table is shown below. $$\begin{array} { c | c | c } \text { Sample } & \text { Weights } & \bar { x } \\\hline \mathrm { A } , \mathrm { B } & 290,320 & 305\end{array}$$
Use your table to find the mean of the sample means. Is this mean equal to the mean of the five given weights in the
population?

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Definitions:

Preschool Children

Young children typically aged between three and five years, often undergoing early education before starting compulsory schooling.

Empathize

The capacity to understand and share the feelings of another person from their perspective.

Theory Of Mind

The ability to attribute mental states—beliefs, intents, desires, emotions—to oneself and others, and to understand that others have beliefs, desires, and intentions that are different from one's own.

Conservation

The principle in cognitive development where a child recognizes that quantity remains the same despite changes in its shape or form.