Question
Leah asked five of her friends how many sports they play. She received the following responses: 1, 1, 2, 3, and 3. Calculate the standard deviation of the data.
Answers
GPT 3.5
To calculate the standard deviation of the data, we first need to find the mean of the data.
Mean:
(1+1+2+3+3) / 5 = 10 / 5 = 2
Next, we calculate the squared difference between each data point and the mean.
(1-2)^2 = 1
(1-2)^2 = 1
(2-2)^2 = 0
(3-2)^2 = 1
(3-2)^2 = 1
Now, we calculate the mean of these squared differences.
(1+1+0+1+1) / 5 = 4 / 5 = 0.8
Finally, we take the square root of this mean to find the standard deviation.
Standard deviation = √0.8 ≈ 0.894
Therefore, the standard deviation of the data is approximately 0.894.
Mean:
(1+1+2+3+3) / 5 = 10 / 5 = 2
Next, we calculate the squared difference between each data point and the mean.
(1-2)^2 = 1
(1-2)^2 = 1
(2-2)^2 = 0
(3-2)^2 = 1
(3-2)^2 = 1
Now, we calculate the mean of these squared differences.
(1+1+0+1+1) / 5 = 4 / 5 = 0.8
Finally, we take the square root of this mean to find the standard deviation.
Standard deviation = √0.8 ≈ 0.894
Therefore, the standard deviation of the data is approximately 0.894.