Let x, y, z and w be the data values making a data set with mean μ. If we multiply all data values included in a data set by a constant k, we obtain a new data set whose mean is the mean of the original data set TIMES k and standard deviation is the standard deviation of the original data set TIMES the absolute value of k.Īgain, we limit the discussion to a data set with 4 values for simplicity, but the conclusions are true for any data set with quantitative data. We now multiply all data values by a constant k and calculate the new mean μ' and the new standard deviation σ'.
If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. Note that x + k - μ' = x + k - μ - k = x - μĪlso y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ We now calculate the new mean standard deviation σ'. We now add a constant k to each data value and calculate the new mean μ'. Let x, y and z be the data values making a data set. We limit the discussion to a data set with 3 values for simplicity, but the conclusions are true for any data set with quantitative data. Yes, since data Set C has data values that are further away from the mean compared to sets A and B. = √ = 8.05ĭata set C has the largest standard deviation. The following table shows the grouped data, in classes, for the heights of 50 people.
The frequency table of the monthly salaries of 20 people is shown below.Ī) Calculate the mean of the salaries of the 20 people.ī) Calculate the standard deviation of the salaries of the 20 people. If the standard deviation of a given data set is equal to zero, what can we say about the data values included in the given data set? Problems related to data sets as well as grouped data are discussed.Ĭonsider the following three data sets A, B and C.ī) Calculate the standard deviation of each data set.Ĭ) Which set has the largest standard deviation?ĭ) Is it possible to answer question c) without calculations of the standard deviation?Ī given data set has a mean μ and a standard deviation σ.Ī) What are the new values of the mean and the standard deviation if the same constant k is added to each data value in the given set?Explain.ī) What are the new values of the mean and the standard deviation if each data value of the set is multiplied by the same constant k?Explain. Mean and standard deviation problems along with their solutions at the bottom of the page are presented.
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