# Statistics

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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

• Statistics -

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.

• Statistics -

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.

• Statistics -

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.

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