if a new data point at 12 is added to the graph, which will be true? the mean will increase, and the median…

if a new data point at 12 is added to the graph, which will be true? the mean will increase, and the median will stay the same. the median will increase, and the mean will stay the same. the mean will increase more than the median, but both will increase. the median will increase more than the mean, but both will increase.

if a new data point at 12 is added to the graph, which will be true? the mean will increase, and the median will stay the same. the median will increase, and the mean will stay the same. the mean will increase more than the median, but both will increase. the median will increase more than the mean, but both will increase.

Answer

Answer:

The mean will increase, and the median will stay the same.

Explanation:

Step1: Compter le nombre de données initiales

Il y a 9 données initiales.

Step2: Trouver la médiane initiale

Trier les données : 1, 2, 2, 3, 3, 4, 5, 5, 6. La médiane est 3 (la 5ème valeur après le tri).

Step3: Calculer la moyenne initiale

$\text{Moyenne initiale}=\frac{1 + 2+2+3+3+4+5+5+6}{9}=\frac{31}{9}\approx3.44$

Step4: Ajouter la nouvelle donnée

Ajouter 12. Il y a maintenant 10 données.

Step5: Trouver la nouvelle médiane

Trier les données : 1, 2, 2, 3, 3, 4, 5, 5, 6, 12. La médiane est $\frac{3 + 4}{2}=3.5$ (moyenne des 5ème et 6ème valeurs après le tri).

Step6: Calculer la nouvelle moyenne

$\text{Nouvelle moyenne}=\frac{1 + 2+2+3+3+4+5+5+6+12}{10}=\frac{43}{10}=4.3$

Step7: Analyser les changements

La moyenne augmente de $\approx3.44$ à 4.3. La médiane augmente de 3 à 3.5. La moyenne augmente et la médiane reste relativement stable comparativement.