Measures of Center & Variability - Pre Algebra

1. What is the median of 2, 6, 8, 10?

   $7$. With an even count, average the two middle values: $\frac{6 + 8}{2} = 7$.

2. How is the mean of a data set calculated?

   Add all the values and divide by the number of values.

3. What is the range of 12, 5, 20, 9?

   $15$. Range is maximum minus minimum: $20 - 5 = 15$.

4. Which measure of variability is usually reported with the median?

   The interquartile range (IQR). The mean is usually paired with the mean absolute deviation.

5. What is the median of 3, 9, 4, 12, 5?

   $5$. In order, the values are 3, 4, 5, 9, 12, and 5 is in the middle.

6. What does the mean absolute deviation (MAD) measure?

   The average distance between each data value and the mean of the data set.

7. What is the mean of 4, 7 and 10?

   $7$. $\frac{4 + 7 + 10}{3} = \frac{21}{3} = 7$.

8. Every value in a data set is increased by 5. What happens to the mean absolute deviation?

   It stays the same. Every value and the mean shift by 5, so the distances from the mean do not change.

9. For the data 1, 2, 3, 4, 100, which better describes a typical value: the mean or the median?

   The median, 3. The mean is 22, pulled far up by the outlier 100.

10. What is the mean absolute deviation of 2, 4, 6, 8?

    $2$. The mean is 5, the distances are 3, 1, 1, 3, and their mean is $\frac{8}{4} = 2$.

11. The mean of 5 values is 8. What is the sum of the values?

    $40$. Sum $= \text{mean} \times \text{count} = 8 \times 5 = 40$.

12. Which measure of center is resistant to outliers: the mean or the median?

    The median. An extreme value changes the mean a lot but barely moves the middle value.

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