The Shape of a Distribution (Leaving Cert Mathematics): Quizzes

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The Shape of a Distribution
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In a symmetrical distribution, what is the relationship between mean, median, and mode?

Mean=Median=Mode\text{Mean} = \text{Median} = \text{Mode}

In a positive skew distribution, what is the relationship between mean, median, and mode?

Mean>Median>Mode\text{Mean} > \text{Median} > \text{Mode}

In a negative skew distribution, what is the relationship between mean, median, and mode?

Mean<Median<Mode\text{Mean} < \text{Median} < \text{Mode}

What shape does a symmetrical distribution create when drawn as a smooth line?

Bell-shaped curve

In a positive skew distribution, which direction does the tail extend?

To the right

In a negative skew distribution, which direction does the tail extend?

To the left

Which measure of central tendency is always pulled in the direction of the skew?

Mean

Which is a real-life example of a symmetrical distribution?

Heights of people in a large sample

Which is a real-life example of positive skew?

Income distribution

Which is a real-life example of negative skew?

Exam scores when most students do well

A distribution has its peak on the left and tail on the right. What type is it?

Positive skew

Why is the mean affected more than median in skewed distributions?

Mean is affected by extreme values

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