Solutions for Session 2, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5 | C6| C7| C8

Problem C1

Here's what the completed frequency table should look like:

Raisin Count

Frequency

 25 1 26 2 27 3 28 5 29 4 30 1 31 1

Problem C2

 a. The minimum raisin count is 25 raisins. b. The maximum raisin count is 31 raisins. c. Adding the frequencies results in a total of 10 boxes containing between 26 and 28 raisins. d. All 17 boxes do. e. The count of 28 raisins has the highest frequency, which is five. f. Two boxes contain more than 29 raisins: one has 30 and one has 31. g. Fifteen boxes contain 29 or fewer raisins. h. One box contains fewer than 26 raisins. i. One box contains 25 or fewer raisins. j. Fourteen boxes contain between 26 and 29 raisins.

 Problem C3 Answers vary. Questions about individual raisin counts tend to be easier to answer with a frequency table (as there is no counting required), but questions about ranges of values are often easier with a line plot.

Problem C4

Here's what the completed table should look like:

Raisin Count

Frequency

 25 1 26 3 27 6 28 11 29 15 30 16 31 17

Problem C5

The answers are identical to those in Problem C2.

 a. The minimum raisin count is 25 raisins. b. The maximum raisin count is 31 raisins. c. Adding the frequencies results in a total of 10 boxes containing between 26 and 28 raisins. d. All 17 boxes do. e. The count of 28 raisins has the highest frequency, which is five. f. Two boxes contain more than 29 raisins: one has 30 and one has 31. g. Fifteen boxes contain 29 or fewer raisins. h. One box contains fewer than 26 raisins. i. One box contains 25 or fewer raisins. j. Fourteen boxes contain between 26 and 29 raisins.

 Problem C6 Questions about ranges may be easier with the cumulative frequency table. C5 (d) and (g) in particular are easier, since their answers can be read directly from the table. Questions about individual frequencies are more difficult because they require subtraction to go from the cumulative frequency table to the frequency table.

Problem C7

Here's what the completed table should look like:

Raisin Count

Frequency

Cumulative Frequency

 25 1 1 26 2 3 27 3 6 28 5 11 29 4 15 30 1 16 31 1 17

Problem C8

 a. The cumulative frequency for 30 raisins is 16, and the cumulative frequency for 25 raisins is 1, so the number of boxes containing between 26 and 30 raisins is 15. Note that we use the frequency for 25 raisins as the lower boundary if we want to include 26 in the count. b. The cumulative frequency for 31 raisins is 17, and the cumulative frequency for 26 is 3, so the answer is 14 boxes. c. The cumulative frequency for 28 raisins is 11, so all six other boxes (17-11) must have more than 28 raisins.