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Data Set: 32, 28, 24, 28, 28, 31, 35, 29, 26 a. Calculate the mean, median...

Data Set: 32, 28, 24, 28, 28, 31, 35, 29, 26

a. Calculate the mean, median and mode

b. Based on your answers from Part A, describe how the data is distributed (symmetrical, positively / negatively skewed)

c. Calculate the range

d. Calculate the variance and standard deviation using the definition formula

e. Calculate the variance and standard deviation using the computation formula

math   Statistics-And-Probability   
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Answer #1

(a) The Computation Table 32 28 24 28 28 31 35 29 26 25 36 X,-261 4-X)- 86 The formula for calculating the point estimate of the popul ati on mean is ΣΧ, (261) = Therefore, the point estimate of the population mean is X~ 29 1 The medi an is the middle value. In a list of nine values, that will be the The data are arranged in ascending order X: 24 26 28 28 28 29 31 32 35 The median is the 5th value in the data set Median,M28

The mode is the most frequent value in the data set and it is called as mode Mode,M.28 5) Ezplanation The mean isX-29, which is greater than that of the medi an is M- 28 is calculated in the part [a). The distribution is described as the right skewed distribution c) The data are arranged in ascending order X: 24 26 28 28 28 29 31 32 35 The formula for calculating the range is Range = Maximum-Minimum R 35-24 R=11 Range I Therefore, the range is Range -11

(d) The Computation Table 32 28 24 28 28 25 4 35 29 26 36 5-1 The formula for calculating the sample variance of the sample data is Σ (32-292 + (28-29), +(26-29)2 -1 i-1 (86) 10.75 Var(X)s 10.801 The formula for calculating the standard devi ati on of the sample data is Σ (32-292 + (28-292 + +(26-29)2 o 509+1+.+9) 10.75 3.278719 S 32787 Therefore, the stan dard deviati on of the sample data is s,3 2787

(e) The Computation Table i-1 32 28 24 28 28 31 35 29 26 1024 784 576 784 784 961 1225 841 676 i-1 The formula for calculating the value of the sum of squares is 7655- (261) 7655_ 68121 7655-7569 86 The formula for calculating the value of the sum of squares is SS 86 The formula for calculating the sample variance of the data is N-1 86 86 = 10.75 s 10.75 Therefore, the sample variance ofthe data is s2 10.75 The formula for calculating the standard deviati on of the sample data is 10.75 3.278719 s, 32787 Therefore, the standard deviation of the sample data is s, ч 13.2787

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