Griffin Riley
10/30/2023 · Senior High School
17 . ¿Cuál es la desviación estándar de los datos \( 3,6,7,2,7 \) ? a) \( \sqrt{\frac{22}{5}} \) b) 5 c) 7 d) \( \sqrt{\frac{22}{25}} \)
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Tutor-Verified Answer
Step-by-step Solution
Para calcular la desviación estándar de los datos \( 3, 6, 7, 2, 7 \), seguimos estos pasos:
1. **Calcular la media**:
\[
\text{Media} = \frac{3 + 6 + 7 + 2 + 7}{5} = \frac{25}{5} = 5
\]
2. **Calcular las diferencias al cuadrado**:
\[
(3 - 5)^2 = (-2)^2 = 4
\]
\[
(6 - 5)^2 = (1)^2 = 1
\]
\[
(7 - 5)^2 = (2)^2 = 4
\]
\[
(2 - 5)^2 = (-3)^2 = 9
\]
\[
(7 - 5)^2 = (2)^2 = 4
\]
3. **Sumar las diferencias al cuadrado**:
\[
4 + 1 + 4 + 9 + 4 = 22
\]
4. **Calcular la varianza** (para una muestra, se divide entre \( n-1 \)):
\[
\text{Varianza} = \frac{22}{5} = 4.4
\]
5. **Calcular la desviación estándar**:
\[
\text{Desviación estándar} = \sqrt{4.4} = \sqrt{\frac{22}{5}}
\]
Por lo tanto, la respuesta correcta es:
a) \( \sqrt{\frac{22}{5}} \)
Quick Answer
La desviación estándar es \( \sqrt{\frac{22}{5}} \).
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