2.4 Sigma Notation and Calculating the Arithmetic Mean

A group of children are measured to determine the average height of the group. The results are in the table below. What is the mean height of the group to the nearest hundredth of an inch?

A person compares prices for five automobiles. The results are in the table. What is the mean price of the cars the person has considered?

A customer protection service has obtained 8 bags of candy that are supposed to contain 16 ounces of candy each. The candy is weighed to determine if the average weight is at least the claimed 16 ounces. The results are in given in the table. What is the mean weight of a bag of candy in the sample?

A teacher records grades for a class of 70, 72, 79, 81, 82, 82, 83, 90, and 95. What is the mean of these grades?

A family is polled to see the mean of the number of hours per day the television set is on. The results, starting with Sunday, are 6, 3, 2, 3, 1, 3, and 7 hours. What is the average number of hours the family had the television set on to the nearest whole number?

A city received the following rainfall for a recent year. What is the mean number of inches of rainfall the city received monthly, to the nearest hundredth of an inch? Use the table.

A football team scored the following points in its first 8 games of the new season. Starting at game 1 and in order the scores are 14, 14, 24, 21, 7, 0, 38, and 28. What is the mean number of points the team scored in these eight games?

A sample of 10 prices is chosen from a population of 100 similar items. The values obtained from the sample, and the values for the population, are given in the table and the table respectively.

1. Is the mean of the sample within $1 of the population mean?
2. What is the difference in the sample and population means?

A standardized test is given to ten people at the beginning of the school year with the results given in the table below. At the end of the year the same people were again tested.

1. What is the average improvement?
2. Does it matter if the means are subtracted, or if the individual values are subtracted?

A small class of 7 students has a mean grade of 82 on a test. If six of the grades are 80, 82,86, 90, 90, and 95, what is the other grade?

A class of 20 students has a mean grade of 80 on a test. Nineteen of the students has a mean grade between 79 and 82, inclusive.

1. What is the lowest possible grade of the other student?
2. What is the highest possible grade of the other student?

If the mean of 20 prices is $10.39, and 5 of the items with a mean of $10.99 are sampled, what is the mean of the other 15 prices?