Textbook Question
Mean of Roller Coaster Speeds Listed below are maximum speeds (km/h) of randomly selected roller coasters in the United States. Find the mean.
7076978157151194651176545105
142
views
3. Describing Data Numerically
Mean
1:52 minutesProblem 2.RE.16
Textbook Question
For the four test scores 96, 85, 91, and 86, the first 3 test scores are 20% of the final grade, and the last test score is 40% of the final grade. Find the weighted mean of the test scores.
Verified step by step guidance1
Step 1: Understand the concept of a weighted mean. A weighted mean is calculated by multiplying each value by its respective weight, summing these products, and then dividing by the sum of the weights.
Step 2: Assign weights to each test score. The first three test scores (96, 85, 91) each have a weight of 20% (or 0.2), and the last test score (86) has a weight of 40% (or 0.4).
Step 3: Multiply each test score by its respective weight. For example, calculate 96 × 0.2, 85 × 0.2, 91 × 0.2, and 86 × 0.4.
Step 4: Add the weighted values obtained in Step 3. This gives the numerator of the weighted mean formula.
Step 5: Divide the sum from Step 4 by the total weight. The total weight is 0.2 + 0.2 + 0.2 + 0.4 = 1. This division gives the weighted mean of the test scores.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Weighted Mean
The weighted mean is an average that takes into account the relative importance or weight of each value in a dataset. In this case, different test scores contribute differently to the final grade based on their assigned weights. The formula for the weighted mean is the sum of each score multiplied by its weight, divided by the total of the weights.
Recommended video:
Guided course
04:52
Calculating the Mean
Weights in Grading
Weights in grading refer to the proportionate influence that each component of a course has on the final grade. In this scenario, the first three test scores account for 20% each, while the last test score accounts for 40%. Understanding how these weights are distributed is crucial for calculating the overall performance accurately.
Recommended video:
04:24Constructing Confidence Intervals for Proportions Example 2
Calculation of Averages
Calculating averages involves summing a set of values and dividing by the number of values. For weighted averages, however, each value is multiplied by its respective weight before summing. This method ensures that more significant contributions to the average are appropriately represented, which is essential for accurately reflecting a student's performance based on varying test importance.
Recommended video:
Guided course
04:51Find 5-Number Summary - TI-84 Calculator
Related Videos
Related Practice