Question

Please I need help here I dont know how to solve this

Answer 1

X bar stands for the average of the values of X in the data set, and likewise in the case of Y bar; therefore,

Values of Xbar and Ybar

`\begin{gathered} \bar{X}=(18+20+22+25+31+35+38+40+50)/(9)=(279)/(9)=31 \\ and \\ \bar{Y}=(97)/(9) \end{gathered}`

Then, the answers to the first two columns (top to bottom are)

The first column,
`\begin{gathered} X-\bar{X}=18-31=-13\rightarrow first\text{ cell} \\ X-\bar{X}=20-31=-11\rightarrow\text{ second cell} \\ X-\bar{X}=-9 \\ X-\bar{X}=-6 \\ X-\bar{X}=0 \\ X-\bar{X}=4 \\ X-\bar{X}=7 \\ X-\bar{X}=9 \\ X-\bar{X}=19\rightarrow\text{ ninth cell} \end{gathered}`

Similarly, in the case of the second column

`\begin{gathered} Y-\bar{Y=}14-(97)/(9)=(29)/(9)\rightarrow\text{ first cell} \\ Y-\bar{Y}=14-(97)/(9)=(29)/(9)\rightarrow\text{ second cell} \\ (11)/(9) \\ (2)/(9) \\ -(7)/(9) \\ -(7)/(9) \\ -(16)/(9) \\ -(16)/(9) \\ -(25)/(9)\rightarrow\text{ ninth cell} \end{gathered}`

As for the next two columns,

The third column,

`\begin{gathered} (X-\bar{X})^2=(-13)^2=169\rightarrow\text{ first cell} \\ (X-\bar{X})^2=121\rightarrow\text{ second cell} \\ 81\rightarrow\text{ third cell} \\ 36 \\ 0 \\ 16 \\ 49 \\ 81 \\ 361\rightarrow ninth\text{ cell} \end{gathered}`

Similarly, in the case of the fourth column,

`\begin{gathered} (Y-\bar{Y})^2=(841)/(81)\rightarrow\text{ first cell} \\ (Y-\bar{Y})^2=(841)/(81)\rightarrow\text{ second cell} \\ (121)/(81) \\ (4)/(81) \\ (49)/(81) \\ (49)/(81) \\ (256)/(81) \\ (256)/(81) \\ (625)/(81)\rightarrow\text{ ninth cell} \end{gathered}`

Calculating Sx,Sy, and SxSy

`\begin{gathered} S_x=\sum_n^(x_n-\bar{X})^2=914 \\ S_y=\sum_n^(y_n-\bar{Y})^2=37.55555=(338)/(9) \\ S_xS_y=(308932)/(9) \end{gathered}`