Final answer:
To find the standard deviation, first calculate the mean of the push-up counts. Next, find the difference between each value and the mean, square the differences, and sum them up.
Step-by-step explanation:
We can find the standard deviation using the following formula:
s = sqrt(sum((x - mean)²) / N)
where:
s is the standard deviation
x is a data point
mean is the mean of the data
N is the number of data points
Let's calculate the mean:
mean = (21 + 24 + 24 + 27 + 29) / 5 = 25
Now let's calculate the squared deviations from the mean:
deviations = [(21 - 25)², (24 - 25)², (24 - 25)², (27 - 25)², (29 - 25)²]
deviations = [16, 1, 1, 4, 16]
Finally, divide the sum of the squared differences by the total number of values and take the square root to calculate the standard deviation.
variance = sum(deviations) / N = 38 / 5 = 7.6
standard_deviation = √(variance) = √(7.6) ≈ 2.76
Therefore, the standard deviation of Justin's push-ups is approximately 2.76.
So the answer is a) 2.75.