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.
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.