how to interpret a box - and - whisker plot\nask yourself:\n- where do i find the quartiles?\n- what do the…

how to interpret a box - and - whisker plot\nask yourself:\n- where do i find the quartiles?\n- what do the lengths of the whiskers and box parts mean?\nuse the box - and - whisker plot for problems 1 - 8.\n1. what is the lower extreme?\n2. what is the lower quartile?\n3. what is the median of the data set?\n4. what is the upper quartile?\n5. what is the upper extreme?\n6. what is the range between the lower and upper quartile?\n7. for what range are the data most clustered?\n8. for what range are the data most spread out?\nproblem solving\n9. write a set of 15 scores that this box - and - whisker plot could represent.\nshow your work

how to interpret a box - and - whisker plot\nask yourself:\n- where do i find the quartiles?\n- what do the lengths of the whiskers and box parts mean?\nuse the box - and - whisker plot for problems 1 - 8.\n1. what is the lower extreme?\n2. what is the lower quartile?\n3. what is the median of the data set?\n4. what is the upper quartile?\n5. what is the upper extreme?\n6. what is the range between the lower and upper quartile?\n7. for what range are the data most clustered?\n8. for what range are the data most spread out?\nproblem solving\n9. write a set of 15 scores that this box - and - whisker plot could represent.\nshow your work

Answer

Explanation:

Step1: Identify lower extreme

The lower extreme is the smallest value in the data - set, which is the end - point of the left - hand whisker. From the box - and - whisker plot, the lower extreme is 0.

Step2: Identify lower quartile

The lower quartile ($Q_1$) is the left - hand edge of the box. From the plot, $Q_1 = 10$.

Step3: Identify median

The median ($Q_2$) is the line inside the box. From the plot, $Q_2=22$.

Step4: Identify upper quartile

The upper quartile ($Q_3$) is the right - hand edge of the box. From the plot, $Q_3 = 28$.

Step5: Identify upper extreme

The upper extreme is the largest value in the data - set, which is the end - point of the right - hand whisker. From the plot, the upper extreme is 48.

Step6: Calculate inter - quartile range

The range between the lower and upper quartile is the inter - quartile range (IQR), which is $Q_3−Q_1$. So, $IQR=28 - 10=18$.

Step7: Determine most clustered range

The data is most clustered within the box, which is from the lower quartile to the upper quartile. So the range is from 10 to 28.

Step8: Determine most spread out range

The data is most spread out in the whiskers. The left - hand whisker is from 0 to 10 and the right - hand whisker is from 28 to 48.

Step9: Generate a data set

A set of 15 scores could be: 0, 2, 4, 6, 8, 10, 12, 22, 24, 26, 28, 30, 36, 40, 48.

Answer:

  1. 0
  2. 10
  3. 22
  4. 28
  5. 48
  6. 18
  7. 10 - 28
  8. 0 - 10 and 28 - 48
  9. 0, 2, 4, 6, 8, 10, 12, 22, 24, 26, 28, 30, 36, 40, 48