The data set represents the number of minutes a sample of 27 p...

Question

The data set represents the number of minutes a sample of 27 people exercise each week.

108 139 120 123 120 132 123 131 131

157 150 124 111 101 135 119 116 117

127 128 139 119 118 114 127 142 130

d. Describe the shape of the distribution as symmetric, uniform, skewed left, skewed right, or none of these.

Accepted Answer

All right, hello, everyone. So this question says, a data, or excuse me, a teacher recorded the test scores of 20 students listed here. Based on the data, what is the shape of the distribution? Option A says symmetric. B says uniform. C says skewed left. and D says skewed right. So, to understand the shape of the distribution, we first have to consider if there's a pattern in the test scores, which means that the data set first needs to be sorted. From the lowest value to the highest. So, here, I went ahead and briefly paused the recording, so I could write out the sorted data set. Here, in this case, we can see that the lowest value is 55 and the highest value is 100. So now, with the data sorted in front of you, we can do the step by step analysis. So first, the question is, if any symmetry is noted. And in this case, what's noteworthy is that the data set has a range, as mentioned before, from 55 to 100, but more values are concentrated at the higher end of this range. Specifically, more values tend to be between 90 and 100. The mode Which is the most frequent value, is also 100, which is also the highest number in the range. So In comparing the. Data set given to the mean. While we're not going to calculate the mean here, the fact that there are higher scores. Or the fact that there are more scores in the higher end of the range, suggests that the mean is most likely going to be pulled slightly upward. So what does that tell you about the skew? Well, If If the data set itself, if the values are clustered more towards the right, more towards higher values, What that means is that the left tail. Is going to be longer. Because this represents the fact that there are going to be less data values towards the left, towards the smaller end of the range. So Because there are more high scores clustered near to 100. And a few lower scores pulling the tail to the left, the tail is going to be longer on the left, meaning that this data set is going to be left skewed. Which means option C is your correct answer. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

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Key Concepts

Distribution Shape

Skewness

Descriptive Statistics

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