Question

analyzing data
now practice creating a box - and - whisker plot. the first step is to identify the minimum, maximum, and quartile values. identify these values for the following data set, and write the answers in your notebook.
14 27 9 22 13 19 29 7 24 12 20
remember, with an odd - numbered data set, you exclude the middle value when calculating (q_1) and (q_3).
which of the following box - and - whisker plots correctly displays the data set?
a.
box - and - whisker plot a
b.
box - and - whisker plot b
c.
box - and - whisker plot c

Explanation:

Step1: Ordenar los datos

Ordenamos el conjunto: $7, 9, 12, 13, 14, 19, 20, 22, 24, 27, 29$

Step2: Identificar mínimo y máximo

Mínimo = $7$, Máximo = $29$

Step3: Calcular la mediana (Q₂)

Es el valor central: $\text{Mediana} = 19$

Step4: Calcular Q₁ (mitad inferior)

Usamos datos sin la mediana: $7, 9, 12, 13, 14$. Valor central: $Q_1 = 12$

Step5: Calcular Q₃ (mitad superior)

Usamos datos sin la mediana: $20, 22, 24, 27, 29$. Valor central: $Q_3 = 24$

Step6: Coincidir con el gráfico

El gráfico A tiene estos valores: bigote inferior en 7, borde inferior de la caja en 12, línea central en 19, borde superior de la caja en 24, bigote superior en 29.

Answer:

A. The box-and-whisker plot with minimum 7, median 19, maximum 29, Q₁=12, Q₃=24