Question

select the correct answer.
the box plot below represents the number of hours judy takes to complete a quilt.

hours per quilt

which data set could be represented by this box plot?
a. 22, 27, 38, 34, 24, 32, 33, 30, 39
b. 39, 32, 29, 22, 33, 29, 25, 37, 34
c. 25, 36, 30, 32, 34, 39, 22, 29, 36
d. 32, 36, 27, 30, 22, 35, 39, 28, 34

Explanation:

Step1: Analizar el diagrama de caja

El diagrama de caja muestra:
- Mínimo: 22
- Máximo: 39
- Mediana (línea dentro del rectángulo): 32
- Q1 (extremo izquierdo del rectángulo): ~26 (pero revisando las opciones, la mínima es 22, y el primer cuartil y tercer cuartil deben coincidir con la distribución de los datos).

Step2: Analizar cada opción

- **Opción A**: Datos: 22, 27, 38, 34, 24, 32, 33, 30, 39. Ordenados: 22, 24, 27, 30, 32, 33, 34, 38, 39. Mínimo 22, máximo 39, mediana (5to valor) 32. Q1 (2do valor: 24? No, Q1 es el valor del 25%: para 9 datos, la posición es (9+1)/4 = 2.5, así que (24+27)/2 = 25.5. Q3: posición 7.5, (34+38)/2 = 36. Pero el diagrama de caja tiene Q1 ~26? No, revisar la opción B.
- **Opción B**: Datos: 39, 32, 29, 22, 33, 29, 25, 37, 34. Ordenados: 22, 25, 29, 29, 32, 33, 34, 37, 39. Mínimo 22, máximo 39, mediana (5to valor) 32. Q1: posición 2.5, (25+29)/2 = 27. Q3: posición 7.5, (34+37)/2 = 35.5. No coincide.
- **Opción C**: Datos: 25, 36, 30, 32, 34, 39, 22, 29, 36. Ordenados: 22, 25, 29, 30, 32, 34, 36, 36, 39. Mínimo 22, máximo 39, mediana (5to valor) 32. Q1: posición 2.5, (25+29)/2 = 27. Q3: posición 7.5, (36+36)/2 = 36. No.
- **Opción D**: Datos: 32, 36, 27, 30, 22, 35, 39, 28, 34. Ordenados: 22, 27, 28, 30, 32, 34, 35, 36, 39. Mínimo 22, máximo 39, mediana (5to valor) 32. Q1: posición 2.5, (27+28)/2 = 27.5. Q3: posición 7.5, (35+36)/2 = 35.5. No. Espera, la opción B: ordenados: 22, 25, 29, 29, 32, 33, 34, 37, 39. Mínimo 22, máximo 39, mediana 32. Q1: (25+29)/2 = 27, Q3: (34+37)/2 = 35.5. Pero el diagrama de caja tiene el rectángulo desde ~26 hasta ~36? No, la opción B tiene mediana 32, mínimo 22, máximo 39. Revisar la opción B: datos ordenados: 22, 25, 29, 29, 32, 33, 34, 37, 39. Mínimo 22, máximo 39, mediana 32. Q1: el primer cuartil es el valor del 25%: para 9 datos, la posición es (9+1)*0.25 = 2.5, así que (25 + 29)/2 = 27. Q3: (34 + 37)/2 = 35.5. El diagrama de caja muestra que el rectángulo empieza en ~26 (cercano a 27) y termina en ~36 (cercano a 35.5), y la mediana en 32. Esto coincide.

Wait, maybe I made a mistake. Let's recheck the box plot: the left whisker starts at 22, the box starts at ~26 (but the minimum is 22), the box ends at ~36, and the right whisker ends at 39. The median is 32.

Looking at option B: data points are 39, 32, 29, 22, 33, 29, 25, 37, 34. When sorted: 22, 25, 29, 29, 32, 33, 34, 37, 39. So:

- Minimum: 22 (matches the left whisker start)
- Maximum: 39 (matches the right whisker end)
- Median: 5th value, which is 32 (matches the line in the box)
- Q1 (25th percentile): for 9 data points, the position is (9 + 1) * 0.25 = 2.5, so the average of the 2nd and 3rd values: (25 + 29) / 2 = 27 (close to the start of the box, which is around 26-27)
- Q3 (75th percentile): position (9 + 1) * 0.75 = 7.5, so average of 7th and 8th values: (34 + 37) / 2 = 35.5 (close to the end of the box, around 36)

This matches the box plot's features (min 22, max 39, median 32, Q1 ~27, Q3 ~35.5). Other options:

- Option A: sorted data has min 22, but the 2nd value is 24, which would make Q1 lower, not matching the box start.
- Option C: data includes 36 twice, sorted as 22,25,29,30,32,34,35,36,39. Median 32, but Q1 (25th percentile) would be (25+29)/2=27, Q3 (35+36)/2=35.5, but the max is 39, min 22. Wait, but the data in option C has 36,36, but the box plot's max is 39, which is present. But the median is 32, which matches. Wait, no, option B's data when sorted has median 32, min 22, max 39, and the quartiles match the box.

Wait, maybe the correct option is B? Wait, let's check the original problem's box plot: the left whisker is from 22 to 26 (the start of the box), the box is from 26 to 36, median at 32, right whisker from 36 to 39.

So for a data set, the minimum is 22, maximum 39, median 32, Q1 (25th percentile) around 26, Q3 (75th percentile) around 36.

Let's check option B: sorted data: 22,25,29,29,32,33,34,37,39.

Number of data points: 9.

Q1: position (9+1)*0.25 = 2.5, so value is (25 + 29)/2 = 27 (close to 26? Maybe the plot is approximate).

Q3: position 7.5, (34 + 37)/2 = 35.5 (close to 36).

Median: 5th value, 32 (matches).

Minimum: 22 (matches).

Maximum: 39 (matches).

Yes, option B's data matches the box plot's features.

Answer:

B. 39, 32, 29, 22, 33, 29, 25, 37, 34