Mary's test grades were 81, 89, 86, 86, and 84. Mary's teacher recorded one of her grades incorrectly. Instead of an 89, Mary's second test score should have been a 55. Which measure(s) of central tendency are affected by this change?
Mode will still be 86, but mean and median will be changed. Mean functions very much like a fulcrum (balance point). Going from highest score to lowest will change the median (50th percentile).
Mary's test grades were 73, 86, 89, 84, and 86. Mary's teacher recorded one of her grades incorrectly. Instead of an 86, Mary's second test score should have been an 84. Which measure(s) of central tendency are affected by this change?
To determine which measure(s) of central tendency are affected by this change, let's first understand what measures of central tendency represent. Measures of central tendency are statistical measures that indicate the central or average value of a set of data. Common measures of central tendency include the mean, median, and mode.
1. Mean: The mean is calculated by summing all the values in the dataset and dividing it by the total number of values. In this case, the mean would be affected by the change. So, to determine the mean before the change, we add up the original test scores: 81 + 89 + 86 + 86 + 84 = 426. Since there are five test scores, the mean before the change is 426/5 = 85.2. After the change, we replace the incorrect score (89) with 55. So the sum becomes: 81 + 55 + 86 + 86 + 84 = 392. The new mean is 392/5 = 78.4.
2. Median: The median is the middle value when the data is arranged in ascending or descending order. If there is an even number of data values, the median is the average of the two middle values. The median would also be affected by the change. Before the change, the median can be found by arranging the test scores in ascending order: 81, 86, 86, 89, 84. In this case, the median is the middle value, which is 86. After the change, the new scores would be arranged as: 81, 55, 86, 86, 84. Now the median would be the average of the two middle values, which is (86 + 86) / 2 = 86.
3. Mode: The mode is the value that appears most frequently in the dataset. The mode would not be affected by this change. Before and after the change, the mode is 86, as it appears twice, while all other scores appear only once.
Therefore, the measures of central tendency affected by the change are the mean and the median. The mode remains the same.