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Answer the statistical measures and create a box and whiskers plot for the following set of data., On this question page, you will first be asked to fill in statistical measures, then create a box plot. Once you make adjustments to the box plot, the answer area will appear and you will be able to submit your answers.

4, comma, 7, comma, 7, comma, 9, comma, 9, comma, 10, comma, 13, comma, 13, comma, 15, comma, 16
4,7,7,9,9,10,13,13,15,16
Min:
Q1:
Med:
Q3:
Max:
Create the box plot by dragging the lines:
x
Answer
Attempt 1 out of 2

1 answer

Let's calculate the five-number summary for the given data set:

Data Set: 4, 7, 7, 9, 9, 10, 13, 13, 15, 16

  1. Minimum (Min): The smallest value in the dataset.

    • Min = 4

  2. Maximum (Max): The largest value in the dataset.

    • Max = 16

  3. Median (Med): The middle value of the dataset. Since we have 10 values (an even number), the median is the average of the 5th and 6th values.

    • The 5th value is 9 and the 6th value is 10.
    • Med = (9 + 10) / 2 = 9.5

  4. First Quartile (Q1): The median of the first half of the data (lower half).

    • Lower half: 4, 7, 7, 9, 9
    • Q1 is the median of 4, 7, 7, 9, 9 (the 3rd value).
    • Q1 = 7

  5. Third Quartile (Q3): The median of the second half of the data (upper half).

    • Upper half: 10, 13, 13, 15, 16
    • Q3 is the median of 10, 13, 13, 15, 16 (the 3rd value).
    • Q3 = 13

Summary of Statistical Measures:

  • Min: 4
  • Q1: 7
  • Med: 9.5
  • Q3: 13
  • Max: 16

Box Plot Creation

To create the box plot, you need to represent these statistical measures visually. The box will extend from Q1 to Q3, with a line at the median (Med). The "whiskers" will extend from the minimum to Q1 and from Q3 to the maximum.

  1. Draw a box from Q1 (7) to Q3 (13).
  2. Draw a line at the median (9.5) inside the box.
  3. Extend a line (whisker) from the left side of the box (Q1) down to the minimum (4).
  4. Extend a line (whisker) from the right side of the box (Q3) up to the maximum (16).

Make sure everything is proportionally spaced when creating your box plot.