Given the data set 1; 3; 4; 4; 4; 6; 10; 13; 15
1. Determine the mean
2. Determine the mode
3. Determine the median
4. Determine the upper quartile.
5. Determine the standard deviation
6.
1. Mean: (1+3+4+4+4+6+10+13+15) /9 = 60 / 9 = 6.67
2. Mode: The mode is the number that appears most frequently in the data set. In this case, the mode is 4, as it appears three times, while the other numbers appear only once or twice.
3. Median: The median is the middle number when the data set is ordered from smallest to largest. In this case, the data set ordered from smallest to largest is 1, 3, 4, 4, 4, 6, 10, 13, 15. The middle number is the fourth number, which is 4.
4. Upper Quartile: To find the upper quartile, first find the median of the upper half of the data set. The upper half of the data set is 6, 10, 13, 15. The median of the upper half is the average of the two middle numbers, 10 and 13. (10+13) / 2 = 23 / 2 = 11.5
5. Standard Deviation: To find the standard deviation, first calculate the mean (6.67) of the data set. Then, calculate the squared difference between each data point and the mean, sum the squared differences, divide by the total number of data points minus 1, and take the square root of the result. This calculation is typically done using a statistical calculator or software.
6. Additional calculations could include finding the lower quartile, interquartile range, variance, or range depending on the specific needs of the analysis.