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What is the standard deviation for the set of data in the ta Score & 16 & 17 & 18 & 19 & 20 Freq. & 2 & 8 & 11 & 6 & 3 1.06 1.41 3.29 3.67

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What is the standard deviation for the set of data in the ta

 Score & 16 & 17 & 18 & 19 & 20 
 Freq. & 2 & 8 & 11 & 6 & 3 


1.06
1.41
3.29
3.67

What is the standard deviation for the set of data in the ta Score & 16 & 17 & 18 & 19 & 20 Freq. & 2 & 8 & 11 & 6 & 3 1.06 1.41 3.29 3.67

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ScarlettExpert · Tutor for 3 years

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#Explanation<br />The standard deviation is a measure of the amount of variation or dispersion in a set of values. It is calculated using the following steps:<br /><br />1. Compute the mean (average) of the data set.<br />2. Subtract the mean from each data point and square the result.<br />3. Compute the mean of these squared differences.<br />4. Take the square root of the result from step 3.<br /><br />Given the frequency table, we can calculate the mean as follows:<br /><br />Mean = Σ(score * frequency) / Σ(frequency)<br /><br />Then, we calculate the variance (the square of the standard deviation) as follows:<br /><br />Variance = Σ[(score - mean)² * frequency] / Σ(frequency)<br /><br />Finally, we find the standard deviation by taking the square root of the variance.<br /><br />#Answer<br />Let's calculate the mean first:<br /><br />Mean = (16*2 + 17*8 + 18*11 + 19*6 + 20*3) / (2+8+11+6+3) = 18.1<br /><br />Next, we calculate the variance:<br /><br />Variance = [(16-18.1)²*2 + (17-18.1)²*8 + (18-18.1)²*11 + (19-18.1)²*6 + (20-18.1)²*3] / (2+8+11+6+3) = 1.29<br /><br />Finally, we find the standard deviation by taking the square root of the variance:<br /><br />Standard Deviation = √1.29 = 1.14<br /><br />So, the closest option to our calculated standard deviation is option2: 1.41.
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