Final answer:
a. The arithmetic mean is 21.55 grams. b. The interquartile range is 6 grams. c. The standard deviation is 5.07 grams. d. The boxplot can be constructed using the given values.
Step-by-step explanation:
a. To find the arithmetic mean, we add up all the values in the sample and divide by the number of values. In this case, the sum of all the carbohydrate amounts is 237 grams. Dividing by 11 (the number of servings) gives us an arithmetic mean of 21.55 grams.
b. To find the interquartile range, we first need to arrange the data in ascending order. The sorted data is 11, 15, 15, 17, 19, 20, 21, 22, 23, 25, 29. The lower quartile is the median of the lower half of the data, which is 17. The upper quartile is the median of the upper half of the data, which is 23. The interquartile range is the difference between the upper and lower quartiles, which is 6 grams.
c. To find the standard deviation, we first calculate the mean of the sample, which is 21.55 grams (as found in part a). Then, for each value in the sample, we subtract the mean, square the result, and sum up all these squared differences. Dividing this sum by the number of values minus 1 (11-1=10) gives us the variance. The standard deviation is the square root of the variance, which is 5.07 grams.
d. To construct a boxplot, we first need to find the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values of the data. The minimum is 11 grams, Q1 is 17 grams, Q2 (median) is 21 grams, Q3 is 23 grams, and the maximum is 29 grams. Using this information, we can draw a horizontal line from Q1 to Q3, with a vertical line at the median. Then, we can extend whiskers (lines) from Q1 to the minimum and from Q3 to the maximum. Any outliers can be marked as points outside the whiskers. A boxplot visually represents the five-number summary of the data.