Calculate the mean, median, and mode for the following data set. Is the distribution normal or skewed? If its skewed, is it positively skewed or negatively skewed? Which of these measures of central tendency would be most appropriate?
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
If normal, the measures of central tendency should be approximately equal. If skewed, the mean is most effected by deviant scores, so the skew will be in the direction of the mean.
Mean = sum of scores/number of scores
Mode = most frequently occurring score
Median = 50% percentile (half of scores valued above and half valued below). Arrange scores in order of value first.
Okay, for the following data set I arranged the scores from lowest to highest. I added all the numbers in the data set and came up with the following
Added all numbers in data set = 3,958
Divide by number of scores = 50
3,958 / 50 = 79.16
Is 79.16 the Mean?
When it came to the Mode the number that was most frequently occurring in the data set is 98. Is 98 the Mode?
When there are 50 scores in a data set how am I supposed to figure out the median? I don't quite understand this about how to come up with the median. The scores are arranged in order of value but I am still quite confused on this part.
I haven't checked your data, but your process is correct for mean and mode.
Arranged in order of value, the median is between the 25th and 26th score, which gives half of the scores valued above and half below.
Just from the mean and mode, the distribution would seem to be negatively skewed.
Of the measures of central tendency for a skewed distribution, the one that is most central of the three would be most appropriate.
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.