QuestionProblem \# 2: (Finding the missing value) Lucy took three tests. If her median score was 82 , her mean score was 87 , and the range was 17 , what were her three test scores? Use two different strategies (the balance method and the equation).
Problem \# 3: (Finding average speed) For the first 3 hours, we drove 72 miles per hour on average. For the next 1 and a half hour, we drove 55 miles per hour. What was our average speed?
Problem \# 4: (Finding overall average) On a certain exam, Mr. Smith graded 10 papers of section A and found that the mean for this group of students was 70 . Then he graded 20 papers of section B and found that the mean for the second group was 80 . Then he graded 25 papers of section C and found that the mean for the third group was 82 . What was the overall mean of the combined group of students?

Studdy Solution
Calculate the average speed:
$$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} = \frac{298.5}{4.5} = 66.33 \text{ miles per hour}$$
The average speed is $66.33$ miles per hour.
### Problem #4: Finding Overall Average
_ASSUMPTIONS_:
1. Section A has 10 papers with a mean of 70.
2. Section B has 20 papers with a mean of 80.
3. Section C has 25 papers with a mean of 82.
_HIGH_LEVEL_APPROACH_:
1. Calculate the total score for each section.
2. Calculate the total number of papers.
3. Find the overall mean.
STEP_1: Calculate the total score for section A:
$$\text{Total Score}_A = 10 \times 70 = 700$$
STEP_2: Calculate the total score for section B:
$$\text{Total Score}_B = 20 \times 80 = 1600$$
STEP_3: Calculate the total score for section C:
$$\text{Total Score}_C = 25 \times 82 = 2050$$
STEP_4: Calculate the total number of papers:
$$\text{Total Papers} = 10 + 20 + 25 = 55$$
STEP_5: Calculate the overall mean:
$$\text{Overall Mean} = \frac{\text{Total Score}_A + \text{Total Score}_B + \text{Total Score}_C}{\text{Total Papers}} = \frac{700 + 1600 + 2050}{55} = 78.18$$
The overall mean is $78.18$.