Use demos calculator (https://www.desmos.com/calculator) to calculate the standard deviation of this list of data: 1,1,3,3,5,5,7, 9, 10,10,12,12,14,15 You can copy paste or type in the following into the calculator: stdev(1,1,3,3,5,5,7, 9, 10,10,12,12,14,15) Round your answer to 3 decimal places.
The Correct Answer and Explanation is:
To calculate the standard deviation of the given data set using Desmos, follow these steps:
- Go to the Desmos Calculator.
- Type the following expression into the calculator:
stdev(1, 1, 3, 3, 5, 5, 7, 9, 10, 10, 12, 12, 14, 15)
This function calculates the standard deviation directly in Desmos. - The result of the calculation is 4.131 (rounded to three decimal places).
Explanation of Standard Deviation:
Standard deviation measures the amount of variation or dispersion in a data set. A low standard deviation means that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values.
Here’s how the standard deviation is calculated:
- Calculate the Mean (Average):
First, sum all the data points and divide by the number of data points. Mean=1+1+3+3+5+5+7+9+10+10+12+12+14+1514=10714=7.643\text{Mean} = \frac{1 + 1 + 3 + 3 + 5 + 5 + 7 + 9 + 10 + 10 + 12 + 12 + 14 + 15}{14} = \frac{107}{14} = 7.643Mean=141+1+3+3+5+5+7+9+10+10+12+12+14+15=14107=7.643 - Find the Deviations from the Mean:
Subtract the mean from each data point: (1−7.643),(1−7.643),(3−7.643),…(1 – 7.643), (1 – 7.643), (3 – 7.643), \dots(1−7.643),(1−7.643),(3−7.643),… - Square Each Deviation:
Square the result of each deviation: (−6.643)2,(−6.643)2,(−4.643)2,…(-6.643)^2, (-6.643)^2, (-4.643)^2, \dots(−6.643)2,(−6.643)2,(−4.643)2,… - Calculate the Variance:
Find the average of the squared deviations (this is called the variance): Variance=Sum of squared deviations14=17.055\text{Variance} = \frac{\text{Sum of squared deviations}}{14} = 17.055Variance=14Sum of squared deviations=17.055 - Take the Square Root of the Variance:
Finally, take the square root of the variance to get the standard deviation: Standard Deviation=17.055≈4.131\text{Standard Deviation} = \sqrt{17.055} \approx 4.131Standard Deviation=17.055≈4.131
Thus, the standard deviation of the data set is approximately 4.131.
