Lab1_CentralTendency

Mean 444 the mean shows the average number of

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these sample statistics below and provide a brief interpretation. mean: 4.44 The mean shows the average number of delinquencies. median: 4 The median is less affected by skew, which shows that this value is exactly in the middle. 4. Refer to the output from Question 2 to find the following sample statistics. Be sure to provide an interpretation of each. a. Find the mode. (Hint: use the relative frequencies to identify the modal number of delinquent acts.) The mode is 2, which shows that the most frequently occurring number of delinquencies is not that high. b. As one way to measure the dispersion, find the range and the interquartile range. Compute it by hand, using the frequency distribution from Question 2. Show your work and provide an interpretation. (Be sure to label.) Range: 15-0=15 The range is fairly large when it comes to the number of delinquencies the person made. Innerquartile range: 1Q= (1/4)Nth=50/4 th =12.5 th =13 th =2 3Q=(3/4)Nth= (3*50)/4=37.5 th = 38 th =7 3Q-1Q= 7-2= 5 The innerquartile range shows that the data is most likely right skewed, because it isn’t that high. c. As another way to measure the dispersion, find the variance and standard deviation. Compute them by hand, using the frequency distribution from Question 2. (Be sure to label these.) Provide a brief interpretation of the standard deviation. xbar= 4.44 x f xf x-xbar (x- xbar)^2 f*(x-xbar)^2 0 2 0 -4.44 19.7136 39.4272 1 6 6 -3.44 11.8336 71.0016 2 12 24 -2.44 5.9536 71.4432 3 3 9 -1.44 2.0736 6.2208

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4 7 28 -0.44 0.1936 1.3552 5 2 10 0.56 0.3136 0.6272 6 4 24 1.56 2.4336 9.7344 7 6 42 2.56 6.5536 39.3216 8 4 32 3.56 12.6736 50.6944 9 1 9 4.56 20.7936 20.7936 10 1 10 5.56 30.9136 30.9136 13 1 13 8.56 73.2736 73.2736 15 1 15 10.56 111.5136 111.5136 Sum= 50 Sum= 526.32 Variance S^2= 10.74122 Std Dev S= 3.277381 5. Now use Stata to check your work. Again, type summarize delinq, detail . Check
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