 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Solutions for Session 3, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5    Problem C1

 a. Adding the percentages shows us that 90.4% of the responses are in the 70s and below. b. Adding the percentages shows us that 9.6% are 80 or higher. c. Adding the percentages shows us that 42.3% are in the 50s and below. d. Adding the percentages shows us that 57.7% are 60 or higher. e. All of them (100%) are less than 100. f. Adding the percentages shows us that 69.2% are at least 40 but below 70. g. This question cannot be answered using only this relative frequency table, since we are not told how many responses are in the interval 65 to < 70; we only know how many are in the interval 60 to <70. h. This question cannot be answered using only this relative frequency table, since we do not know how many responses are in the interval 30 to < 35. i. This question cannot be answered using only this relative frequency table, since we do not know how many responses are exactly 60 -- only that 34.6% are in the interval 60 to < 70.   Problem C2 For questions (g) and (h), we might guess that half the responses will be in the lower range (60-64 and 30-34) and the other half will be in the upper range (65-69 and 35-39). For question (g), we know that 23.1% of the responses are 70 or above and 34.6% are in the interval 60 to < 70. Half of 34.6% is 17.3%, which gives us an estimate of 23.1% + 17.3% = 40.4% for the percentage of responses that are 65 or greater. For question (h), we know that 7.7% of the responses are in the interval 30 to < 40. Half of this is 3.85% (or 3.9%), which is our estimate for the percentage of responses less than 35.   Problem C3

Here is the completed table:  Interval Frequency Cumulative Frequency  30 to < 40 4 4 40 to < 50 1 5 50 to < 60 17 22 60 to < 70 18 40 70 to < 80 7 47 80 to < 90 4 51 90 to < 100 1 52    Problem C4

 a. Forty-seven responses are in the 70s and below. b. Five responses are 80 or higher (52 - 47). c. Twenty-two responses are in the 50s and below. d. Thirty responses are 60 or higher (52 - 22). e. All 52 responses are less than 100. f. Thirty-six responses are at least 40 but less than 70 (40 - 4).

Questions (g), (h), and (i) cannot be answered because the table only gives answers in intervals of 10, and these questions ask about smaller intervals.   Problem C5

 a. Using only the relative cumulative frequencies, 90.4% of the responses are in the 70s and below. b. Using only the relative cumulative frequencies, 9.6% of the responses are 80 or higher (100 - 90.4). c. Using only the relative cumulative frequencies, 42.3% of the responses are in the 50s and below. d. Using only the relative cumulative frequencies, 57.7% of the responses are 60 or higher (100 - 42.3). e. All of the responses (100%) are less than 100. f. Using only the relative cumulative frequencies, 69.2% of the responses are at least 40 but less than 70 (76.9 - 7.7).     