Answer :
The correct answer among the ones you provided is 6.2 inches. This means that, on average, the heights of the players deviate by about 6.2 inches from the mean height.
The term "deviation" in statistics refers to how much each value in a set of data differs from the mean (or average) of the data. The "standard deviation" gives us a measure of how spread out the values in a data set are from the mean.
Here are the steps to calculate the sample standard deviation:
1. First, we find the mean of the heights. We add up all the heights (in inches) and divide by the number of players. For this team, we have:
(67 + 72 + 76 + 76 + 84) / 5
= 375 / 5
= 75 inches
So, the average (mean) height of the players is 75 inches.
2. Next, we find the deviation of each player's height from the mean. We subtract the mean from each height:
Player 1: 67 - 75 = -8 inches
Player 2: 72 - 75 = -3 inches
Player 3: 76 - 75 = 1 inch
Player 4: 76 - 75 = 1 inch
Player 5: 84 - 75 = 9 inches
3. We then square each deviation:
Player 1: (-8)² = 64
Player 2: (-3)² = 9
Player 3: 1² = 1
Player 4: 1² = 1
Player 5: 9² = 81
4. Next, we find the mean of these squared deviations. This is called the variance. We add up the squared deviations and divide by the number of players minus one (since it's a sample standard deviation):
Variance = (64 + 9 + 1 + 1 + 81) / (5-1) = 156 / 4 = 39
5. Finally, the sample standard deviation is the square root of the variance. Therefore, the standard deviation of the players' heights is √39, which equals approximately 6.2 inches.
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