Justin did push-ups for the past 5 days.The following data points are the number of push-ups he did each day.
$$
21,24,24,27,29
$$

Find the standard deviation of the data set.
Round your answer to the nearest hundredth.
$\square$ push-ups

Question

Justin did push-ups for the past 5 days.The following data points are the number of push-ups he did each day.
$$
21,24,24,27,29
$$

Find the standard deviation of the data set.
Round your answer to the nearest hundredth.
$\square$ push-ups

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the mean of the data set: $\frac{21 + 24 + 24 + 27 + 29}{5} = \frac{125}{5} = 25$. ‖ ‖ step 2 ⋮ Subtract the mean from each data point and square the result: $(21-25)^2$, $(24-25)^2$, $(24-25)^2$, $(27-25)^2$, $(29-25)^2$. ‖ ‖ step 3 ⋮ Sum the squared differences: $16 + 1 + 1 + 4 + 16 = 38$. ‖ ‖ step 4 ⋮ Divide the sum by the number of data points minus one (n-1) for the sample variance: $\frac{38}{5-1} = \frac{38}{4} = 9.5$. ‖ ‖ step 5 ⋮ Take the square root of the variance to find the standard deviation: $\sqrt{9.5} \approx 3.0822$. ‖ ∻Answer∻ ⚹ The standard deviation of the data set is approximately 3.08 push-ups. ⚹ ∻Key Concept∻ ⚹Standard Deviation⚹ ∻Explanation∻ ⚹Standard deviation measures the amount of variation or dispersion in a set of values. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.⚹◊What is the formula for calculating the standard deviation of a data set?⍭ Generate me a similar question◊

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