Q. For the following set of data, find the sample standard deviation, to the nearest hundredth. 146,147,144,117,105,105,89
List and Verify Data: List the data set and verify the numbers.Data set: 146,147,144,117,105,105,89Check for any input errors in the data set.
Calculate Mean: Calculate the mean (average) of the data set.Mean = (146+147+144+117+105+105+89)/7Mean = 853/7Mean = 121.8571 (rounded to four decimal places for accuracy in further calculations)
Square and Subtract: Subtract the mean from each data point and square the result.(146−121.8571)2=583.2659(147−121.8571)2=631.2659(144−121.8571)2=491.2659(117−121.8571)2=23.5914(105−121.8571)2=283.5914(105−121.8571)2=283.5914(89−121.8571)2=1078.5914
Sum Squared Differences: Sum the squared differences.Sum = 583.2659+631.2659+491.2659+23.5914+283.5914+283.5914+1078.5914Sum = 3374.1633
Calculate Variance: Divide the sum of the squared differences by the sample size minus one to get the variance.Sample size n = 7Variance = Sum/(n−1)Variance = 3374.1633/(7−1)Variance = 3374.1633/6Variance = 562.3606
Calculate Standard Deviation: Take the square root of the variance to get the sample standard deviation.Standard deviation = 562.3606Standard deviation = 23.7159
Round Standard Deviation: Round the standard deviation to the nearest hundredth.Standard deviation (rounded) = 23.72
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