Here are sometimes it took students to complete a Statistics final exam (in minu

Question

Here are sometimes it took students to complete a Statistics final exam (in minutes): 60, 60, 50,120,90,120, 50, 180, 180, 120, 180, 60,120,90,300 Complete a 5-number summary for this data (min, Q1, median, Q3, max) and calculate the IQR. Determine if any data point is "unusual". One way is to use the IQR and Q3: Any data point GREATER THANQ3 + 1.5* IQR is considered "unusual". Another way is to calculate the mean and standard deviation then, any data value more than 2 standard deviations from the mean is considered "unusual". DO IT BOTH WAYS. (You have done enough tedious calculations so the mean is 106 and the standard deviation is 68).Anything "unusual"?

Explanation / Answer

Arrange the data in to smallest to largest

Five number summary is

minimum value =50;Q1 = 60;Median = 120; Q3=180; maximum value =120;

Mean = 1780/15 =118.67; standard deviaiton = 68.4

Inter quartile range = 180-60=120

Q1- 1.5*IQR=60-(1.5*120) = -120 and Q3+1.5 IQR =60+(1.5*120)=240

one outliers i.e 300 present in the data

Z-values for the given data, where z= x- mean/Sd

here the z value corresponding to 300 is more than 2 standard deviations. so this is the outlier.

50 50 60 60 60 90 90 120 120 120 120 180 180 180 300

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