Pregunta
Find the standard deviation for the group of data items. \[ 9,10,11,12,13 \]
Ask by Pierce Clark. in the United States
Feb 26,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The standard deviation is approximately 1.414.
Solución
To find the standard deviation for the data set 9, 10, 11, 12, 13, follow these steps:
1. Calculate the mean (average):
Mean = (9 + 10 + 11 + 12 + 13) / 5 = 55 / 5 = 11
2. Subtract the mean from each number to find the deviation:
9 - 11 = -2
10 - 11 = -1
11 - 11 = 0
12 - 11 = 1
13 - 11 = 2
3. Square each deviation:
(-2)² = 4
(-1)² = 1
0² = 0
1² = 1
2² = 4
4. Find the variance by averaging these squared differences:
Variance = (4 + 1 + 0 + 1 + 4) / 5 = 10 / 5 = 2
5. Take the square root of the variance to get the standard deviation:
Standard Deviation = √2 ≈ 1.414
Thus, the standard deviation for the group of data items is approximately 1.414.
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg


Beyond the Answer
To find the standard deviation, first calculate the mean (average): Mean = (9 + 10 + 11 + 12 + 13) / 5 = 11. Next, find the squared differences from the mean: - (9 - 11)² = 4 - (10 - 11)² = 1 - (11 - 11)² = 0 - (12 - 11)² = 1 - (13 - 11)² = 4 Now, add those squared differences: 4 + 1 + 0 + 1 + 4 = 10. To find the variance, divide by the number of data points: Variance = 10 / 5 = 2. Finally, take the square root of the variance to find the standard deviation: Standard Deviation = √2 ≈ 1.41.

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium