Final answer:
To compute the descriptive statistics for the bowler's scores (range, variance, standard deviation, and coefficient of variation), we first find the mean, subtract the mean from each score, square the result, find the sum of squared differences, and then calculate the corresponding values. The range is 22, the variance is 70.67, the standard deviation is approximately 8.41, and the coefficient of variation is approximately 4.73%.
Step-by-step explanation:
To compute the descriptive statistics for the bowler's scores, let's first find the range. The range is the difference between the highest and lowest scores. In this case, the highest score is 190 and the lowest score is 168, so the range is 190 - 168 = 22. To find the variance and standard deviation, we need to find the mean of the scores first. Adding up all the scores gives us a sum of 182 + 168 + 184 + 190 + 170 + 174 = 1068. Dividing this sum by the number of scores (6) gives us a mean of 1068 / 6 = 178.
Next, we subtract the mean from each score, square the result, and find the sum of these squared differences. Dividing this sum by the number of scores minus 1 gives us the variance. Lastly, taking the square root of the variance gives us the standard deviation. By following these steps, we find that the variance is 70.67 and the standard deviation is approximately 8.41. To compute the coefficient of variation, we divide the standard deviation by the mean and multiply by 100. In this case, the coefficient of variation is (8.41 / 178) * 100 = approximately 4.73%.