To calculate the mean, median, and mode for the given data set, follow these steps:
Mean:
1. Add up all the values in the data set: 100 + 97 + 99 + 70 + 72 + 75 + 82 + 68 + 85 + 88 + 71 + 77 + 93 + 94 + 54 + 59 + 83 + 87 + 98 + 84 + 72 + 96 + 98 + 89 + 74 + 98 + 77 + 82 + 83 + 98 + 90 + 95 + 85 + 76 + 62 + 72 + 36 + 21 + 42 + 86 + 75 + 42 + 91 + 90 + 81 + 78 + 79 + 74 + 82 + 98 = 3860.
2. Divide the sum by the total number of values (50 in this case): 3860 / 50 = 77.2. So, the mean is 77.2.
Median:
1. Arrange the values in ascending order: 21, 36, 42, 42, 54, 59, 62, 68, 70, 71, 72, 72, 74, 74, 75, 75, 76, 77, 77, 78, 79, 81, 82, 82, 83, 83, 84, 85, 85, 86, 87, 88, 89, 90, 90, 91, 93, 94, 95, 96, 97, 98, 98, 98, 98, 98, 98, 99, 100.
2. Since there are 50 values, the median will be the average of the 25th and 26th values, which are 83 and 84, respectively. So, (83 + 84) / 2 = 83.5. Thus, the median is 83.5.
Mode:
1. Determine the value(s) that appear(s) most frequently in the data set.
2. In this case, the mode is 98, as it appears 6 times, more often than any other value.
To determine if the distribution is normal or skewed, you can look at the shape of the data set. One way to visualize this is by creating a histogram or a frequency distribution plot. However, since this is not possible for me as a text-based AI, I can provide some analysis based on the measures of central tendency.
Given that the mean (77.2) is lower than the median (83.5), it suggests that the data set might be negatively skewed. This means that the tail of the distribution is skewed towards the lower values.
The most appropriate measure of central tendency to use depends on the specific circumstances and the nature of the data. In this case, since the data set is suspected to be negatively skewed, the median (83.5) might be a more appropriate measure as it is less influenced by outliers or extreme values. However, it is always valuable to consider all measures of central tendency (mean, median, and mode) to understand the distribution comprehensively.