Math  /  Data & Statistics

QuestionGjejme¨ shume¨ kuadratike brenda grupeve pe¨r te¨ dhe¨nat e me¨poshtme:\text{Gjejmë shumë kuadratike brenda grupeve për të dhënat e mëposhtme:}
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline & \multicolumn{1}{|c|}{\text{Kafsha e laboratorit}} \\ \cline{2-10} \text{Anestezia} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \text{A} & 0.28 & 0.50 & 0.68 & 0.27 & 0.31 & 0.99 & 0.26 & 0.35 & 0.38 & 0.34 \\ \hline \text{B} & 0.20 & 0.38 & 0.50 & 0.29 & 0.38 & 0.62 & 0.42 & 0.87 & 0.37 & 0.43 \\ \hline \text{C} & 1.23 & 1.34 & 0.55 & 1.06 & 0.48 & 0.68 & 1.12 & 1.52 & 0.27 & 0.35 \\ \hline \end{array}
Pe¨r secilin grup (A, B, C), llogarit shume¨ kuadratike te¨ vlerave.\text{Për secilin grup (A, B, C), llogarit shumë kuadratike të vlerave.}

Studdy Solution

STEP 1

1. We are given three groups of data labeled A, B, and C.
2. We need to calculate the sum of squares for each group.

STEP 2

1. Calculate the mean for each group.
2. Compute the squared deviation from the mean for each data point in each group.
3. Sum the squared deviations for each group.

STEP 3

Calculate the mean for group A:
Mean of A=0.28+0.50+0.68+0.27+0.31+0.99+0.26+0.35+0.38+0.3410=0.436\text{Mean of A} = \frac{0.28 + 0.50 + 0.68 + 0.27 + 0.31 + 0.99 + 0.26 + 0.35 + 0.38 + 0.34}{10} = 0.436

STEP 4

Calculate the mean for group B:
Mean of B=0.20+0.38+0.50+0.29+0.38+0.62+0.42+0.87+0.37+0.4310=0.446\text{Mean of B} = \frac{0.20 + 0.38 + 0.50 + 0.29 + 0.38 + 0.62 + 0.42 + 0.87 + 0.37 + 0.43}{10} = 0.446

STEP 5

Calculate the mean for group C:
Mean of C=1.23+1.34+0.55+1.06+0.48+0.68+1.12+1.52+0.27+0.3510=0.86\text{Mean of C} = \frac{1.23 + 1.34 + 0.55 + 1.06 + 0.48 + 0.68 + 1.12 + 1.52 + 0.27 + 0.35}{10} = 0.86

STEP 6

Compute the squared deviations for group A:
\begin{align*} (0.28 - 0.436)^2 & = 0.024576, \\ (0.50 - 0.436)^2 & = 0.004096, \\ (0.68 - 0.436)^2 & = 0.059536, \\ (0.27 - 0.436)^2 & = 0.027556, \\ (0.31 - 0.436)^2 & = 0.015876, \\ (0.99 - 0.436)^2 & = 0.307216, \\ (0.26 - 0.436)^2 & = 0.031056, \\ (0.35 - 0.436)^2 & = 0.007396, \\ (0.38 - 0.436)^2 & = 0.003136, \\ (0.34 - 0.436)^2 & = 0.009216 \end{align*}

STEP 7

Compute the squared deviations for group B:
\begin{align*} (0.20 - 0.446)^2 & = 0.060076, \\ (0.38 - 0.446)^2 & = 0.004356, \\ (0.50 - 0.446)^2 & = 0.002916, \\ (0.29 - 0.446)^2 & = 0.024556, \\ (0.38 - 0.446)^2 & = 0.004356, \\ (0.62 - 0.446)^2 & = 0.030276, \\ (0.42 - 0.446)^2 & = 0.000676, \\ (0.87 - 0.446)^2 & = 0.180276, \\ (0.37 - 0.446)^2 & = 0.005776, \\ (0.43 - 0.446)^2 & = 0.000256 \end{align*}

STEP 8

Compute the squared deviations for group C:
\begin{align*} (1.23 - 0.86)^2 & = 0.1369, \\ (1.34 - 0.86)^2 & = 0.2304, \\ (0.55 - 0.86)^2 & = 0.0961, \\ (1.06 - 0.86)^2 & = 0.04, \\ (0.48 - 0.86)^2 & = 0.1444, \\ (0.68 - 0.86)^2 & = 0.0324, \\ (1.12 - 0.86)^2 & = 0.0676, \\ (1.52 - 0.86)^2 & = 0.4356, \\ (0.27 - 0.86)^2 & = 0.3481, \\ (0.35 - 0.86)^2 & = 0.2601 \end{align*}

STEP 9

Sum the squared deviations for group A:
Sum of squares for A=0.024576+0.004096+0.059536+0.027556+0.015876+0.307216+0.031056+0.007396+0.003136+0.009216=0.48966\text{Sum of squares for A} = 0.024576 + 0.004096 + 0.059536 + 0.027556 + 0.015876 + 0.307216 + 0.031056 + 0.007396 + 0.003136 + 0.009216 = 0.48966

STEP 10

Sum the squared deviations for group B:
Sum of squares for B=0.060076+0.004356+0.002916+0.024556+0.004356+0.030276+0.000676+0.180276+0.005776+0.000256=0.31352\text{Sum of squares for B} = 0.060076 + 0.004356 + 0.002916 + 0.024556 + 0.004356 + 0.030276 + 0.000676 + 0.180276 + 0.005776 + 0.000256 = 0.31352

STEP 11

Sum the squared deviations for group C:
Sum of squares for C=0.1369+0.2304+0.0961+0.04+0.1444+0.0324+0.0676+0.4356+0.3481+0.2601=1.7916\text{Sum of squares for C} = 0.1369 + 0.2304 + 0.0961 + 0.04 + 0.1444 + 0.0324 + 0.0676 + 0.4356 + 0.3481 + 0.2601 = 1.7916
The sums of squares for each group are:
- Group A: 0.48966 \boxed{0.48966} - Group B: 0.31352 \boxed{0.31352} - Group C: 1.7916 \boxed{1.7916}

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