Calculating Averages
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ISEE Middle Level: Quantitative Reasoning › Calculating Averages
What is the mean daily temperature from 61, 63, 62, 60, 61, 47, 62?
59
61
62
416
Explanation
This question tests middle school quantitative reasoning skills, specifically calculating the average from a data set. The average, or mean, is found by adding up all the numbers in a data set and then dividing by the number of values. In this scenario, you need to calculate the average of seven daily temperatures: 61, 63, 62, 60, 61, 47, 62. Adding these temperatures gives 416, and dividing by 7 yields approximately 59.43, which rounds to 59. Choice A is correct because it represents the properly rounded average temperature. The outlier of 47 degrees significantly lowers the average compared to the other temperatures clustering around 61-63. To help students, emphasize the importance of including all data points and practice recognizing how outliers affect the mean in real-world contexts like weather data.
What would the average be without the outlier 2 in 18, 19, 20, 18, 2, 19?
16
18
19
96
Explanation
This question tests middle school quantitative reasoning skills, specifically calculating the average after removing an outlier from a data set. The average, or mean, is found by adding up all the numbers in a data set and then dividing by the number of values. In this scenario, you need to calculate the average of 18, 19, 20, 18, 19 after removing the outlier 2. Adding these five remaining values gives 94, and dividing by 5 yields 18.8, which rounds to 19. Choice B is correct because it accurately reflects the mean without the outlier. With the outlier included, the average would drop to 16, demonstrating the significant impact of extreme values. To help students master this concept, practice identifying outliers using visual representations like dot plots and calculating averages both with and without outliers.
What would the average be without the outlier 95 in 68, 70, 72, 69, 71, 95?
69
70
72
74
Explanation
This question tests middle school quantitative reasoning skills, specifically calculating the average after removing an outlier from a data set. The average, or mean, is found by adding up all the numbers in a data set and then dividing by the number of values. In this scenario, you need to calculate the average of the data set 68, 70, 72, 69, 71 after removing the outlier 95. Adding these five remaining values gives 350, and dividing by 5 yields exactly 70. Choice B is correct because it accurately reflects the mean without the outlier. This demonstrates how outliers can significantly affect averages - with the outlier included, the average would be about 74.2. To help students, practice identifying outliers and understanding their impact on statistical measures, using real-world examples like unusually high or low test scores.