Interpreting Box Plots - Pre Algebra

1. What five values make up the five-number summary shown in a box plot?

   The minimum, the first quartile $Q_1$, the median, the third quartile $Q_3$ and the maximum.

2. About what percent of the data lies above the third quartile?

   About $25\%$. The upper whisker covers the top quarter of the data.

3. What part of a data set does the box of a box plot cover?

   The middle $50\%$ of the data, from the first quartile $Q_1$ to the third quartile $Q_3$.

4. A box plot's whiskers extend from 2 to 11. What is the range of the data?

   $9$. Range is maximum minus minimum: $11 - 2 = 9$.

5. How is the interquartile range (IQR) calculated?

   $\text{IQR} = Q_3 - Q_1$. It measures the spread of the middle half of the data.

6. About what percent of the data lies between the first quartile and the median?

   About $25\%$. The quartiles and median split the data into four parts with about one quarter in each.

7. A box plot has $Q_1 = 30$ and $Q_3 = 40$. Using the $1.5 \times \text{IQR}$ rule, is the value 58 an outlier, and why?

   58 is an outlier. The upper limit is $40 + 1.5(10) = 55$, and 58 is greater than 55.

8. A box plot of test scores has a median of 70. About what fraction of the scores are 70 or below?

   About half. The median splits the data into two halves.

9. In a box plot, the right whisker is much longer than the left whisker. What does this suggest?

   The top quarter of the data is more spread out than the bottom quarter, so the data may be skewed right.

10. A box plot has $Q_1 = 4$ and $Q_3 = 8$. What is the IQR?

    $4$. $8 - 4 = 4$.

11. A box plot has $Q_1 = 10$ and $Q_3 = 20$. Using the $1.5 \times \text{IQR}$ rule, above what value is a data point an outlier?

    35. The IQR is 10, and $Q_3 + 1.5(10) = 20 + 15 = 35$.

Study these flashcards