Here’s a breakdown of each question in your worksheet and guidance to solve them:

Question 9

You're asked to draw a box plot for the data set:

• Data: $\{26, 22, 31, 36, 22, 27, 15, 36, 32, 29, 30\}$.

  1. Order the Data: Arrange the numbers in ascending order: $\{15, 22, 22, 26, 27, 29, 30, 31, 32, 36, 36\}$.
  2. Find Quartiles:
     • Median (Q2): The middle value of the dataset, which is 29.
     • Q1 (First Quartile): The median of the lower half (before the median), which is 22.
     • Q3 (Third Quartile): The median of the upper half (after the median), which is 32.
  3. Identify Extremes: The minimum value is 15, and the maximum is 36.
  4. Draw the Box Plot: Mark these points on a number line and create a box from Q1 to Q3 with a line through the median. Extend "whiskers" from the minimum to Q1 and Q3 to the maximum.

Question 10

For the height of waves data, you need to create a box plot using these values:

• Data: $\{80, 51, 77, 72, 55, 65, 42, 68, 67, 87, 61, 73, 59\}$.

  1. Order the Data: $\{42, 51, 55, 59, 61, 65, 67, 68, 72, 73, 77, 80, 87\}$.
  2. Calculate Quartiles:
     • Median (Q2): 67.
     • Q1: 55.
     • Q3: 73.
  3. Extremes: Minimum is 42 and maximum is 87.
  4. Box Plot: Draw with these values on the number line.

Question 11

This question is about analyzing the box plot of Math Test Scores.

1. Greatest Test Score: The upper extreme of the box plot indicates the highest score.
2. Median Position Explanation: If the median is not centered in the box, it means the data is skewed. For example, more scores could be closer to the lower quartile.
3. Scores Between 71 and 96: Look at what percentage of the data falls in this range based on the box plot.
4. Half of the Scores Above: The median represents the point where half the scores lie above.

Question 12

For the Words Typed Per Minute data, you need to calculate the median, Q1, Q3, and interquartile range.

• Data: $\{80, 42, 65, 72, 63, 81, 67, 73, 40, 51, 68, 59, 77, 55, 78\}$.

1. Order the Data: Arrange in ascending order.
2. Calculate Median.
3. Find Q1 and Q3.
4. Determine Interquartile Range (IQR): $\text{IQR} = Q3 - Q1$.
5. Create Box Plot: Draw using the five-number summary.

Would you like a more detailed calculation for any of these questions?

5 Questions to Explore Further:

1. How do outliers affect the box plot?
2. Why is the interquartile range (IQR) useful in statistics?
3. What does it mean if the median is closer to Q1 or Q3 in a box plot?
4. How can box plots indicate data skewness?
5. Why might a box plot be more informative than just listing quartiles?

Tip

Always double-check the data arrangement in ascending order before calculating quartiles and medians, as even a small error can affect the final plot.