last pay period are given below: 1470 1470 1510 1520 1520 1550 1580 1620 1630 1710 1770 1780 1780 1780 1870 1890 1950 1970 1980 1990 2040 2160 2160 2280 2330 2340 2360 a. Use the percentile locator formula to determine the quartiles (do NOT use the intuitive approach). b. Determine the interquartile range. IQR- c. Describe the shape of the box plot in terms of skewness. Positively Skewed Negatively Skewed
The first quartile Q1 is the 25th percentile The first quartile Q1 is the median of the lower half not including the value of Q2. data values less than the position of the median are
Because there are an odd numbers,so one middle number is = 1580
The second quartile Q2 is the 50th percentile The second quartile Q2 =median=middle number in a sorted data set If there are an odd number of data values, the median is a single number otherwise we take average of the two middle numbers. Since there is an odd number total 27 of data values in this data set, there is only one middle number 14 th value, Therefore, the median is 1780
The third quartile Q3 is the 75th percentile The third quartile Q3 is the median of the upper half not including the value of Q2. data values greater than the position of the median are
1870 , 1890 , 1950 , 1970 , 1980 , 1990 , 2040 , 2160 , 2160 , 2280 , 2330 , 2340 , 2360 ,
Because there are an odd numbers,so one middle number is =2040
Q1 = 1st quartile: 1580
Q2 = Median: 1780
Q3=3rd quartile: 2040
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