(1 point) Calculate the mean and median of the following grades on a math test:
97, 88, 89, 86, 83, 80, 78, 74, 64, 62, 49
Mean =
Median =
Is this data set skewed to the right, symmetric, or skewed to
the left?
(Enter "SKEWED RIGHT", "SYMMETRIC", or "SKEWED LEFT");
To find the mean of the data set, you need to sum up all the values and divide the sum by the total number of values.
Mean = (97 + 88 + 89 + 86 + 83 + 80 + 78 + 74 + 64 + 62 + 49) / 11
Mean = 840 / 11 = 76.36
To find the median of the data set, you need to arrange the values in ascending order and find the middle value.
49, 62, 64, 74, 78, 80, 83, 86, 88, 89, 97
Since we have an odd number of values (11), the median is the middle value, which is 80.
Therefore, the mean of the data set is 76.36 and the median is 80.
To determine if the data set is skewed to the right, symmetric, or skewed to the left, we can compare the mean and median. If the mean is greater than the median, it is skewed to the right. If the mean is less than the median, it is skewed to the left. If the mean is equal to the median, it is symmetric.
In this case, the mean (76.36) is less than the median (80), so the data set is skewed to the left.
To calculate the mean, you need to sum up all the numbers in the data set and then divide by the total number of values.
1. Add up all the numbers: 97 + 88 + 89 + 86 + 83 + 80 + 78 + 74 + 64 + 62 + 49 = 830
2. Divide the sum by the total number of values (which is 11 in this case): 830 / 11 = 75.45
So, the mean of the grades is approximately 75.45.
To find the median, you need to arrange the numbers in ascending order and then find the middle value. If there are an odd number of values, the median is the middle number. If there are an even number of values, the median is the average of the two middle numbers.
1. Arrange the numbers in ascending order: 49, 62, 64, 74, 78, 80, 83, 86, 88, 89, 97
2. Since there are 11 values, the median is the middle number, which is the 6th value: 80
So, the median of the grades is 80.
To determine if the data set is skewed to the right, symmetric, or skewed to the left, you can use the mean and median as indicators.
Since the mean (75.45) is lower than the median (80), it suggests that the data set is skewed to the left.
Median = 50th percentile, middle score in value
Mean = ∑x/n = sum of scores/number of scores