Question

question 2 (1 point)
the data set represents the shoe sizes of 19 students in a fifth grade physical education class.
4,5,5,5,6,6,6,6,7,7,7,7,7.5,7.5,8,8,8.5,8.5,9
create a box plot to represent the distribution of the data.
min: ________
q1: ________
median: ________
q3: ________
max: ________
sketch it on your paper.
blank 1: blank
blank 2: blank
blank 3: blank
blank 4: blank
blank 5: blank

Explanation:

Step1: Order the data

First, we order the given data set: \(4.5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7.5, 7.5, 8, 8, 8.5, 8.5, 9\)

Step2: Find Min

The minimum value (Min) is the smallest number in the data set. Looking at the ordered data, the smallest number is \(4.5\).

Step3: Find Median (Middle value)

Since there are \(n = 19\) data points (odd number), the median is the \(\frac{n + 1}{2}=\frac{19+ 1}{2}=10^{\text{th}}\) value. Counting from the start of the ordered data: the \(10^{\text{th}}\) value is \(7\).

Step4: Find Q1 (First Quartile)

Q1 is the median of the lower half of the data. The lower half consists of the first \(\frac{n - 1}{2}=9\) values (since the median is the \(10^{\text{th}}\) value, we take the first 9 values: \(4.5, 5, 5, 5, 6, 6, 6, 6, 7\)). The median of these 9 values is the \(\frac{9 + 1}{2}=5^{\text{th}}\) value. The \(5^{\text{th}}\) value in this subset is \(6\).

Step5: Find Q3 (Third Quartile)

Q3 is the median of the upper half of the data. The upper half consists of the last \(\frac{n - 1}{2}=9\) values: \(7, 7.5, 7.5, 8, 8, 8.5, 8.5, 9\) (wait, actually, since the median is the \(10^{\text{th}}\) value, the upper half is from the \(11^{\text{th}}\) value to the \(19^{\text{th}}\) value: \(7, 7.5, 7.5, 8, 8, 8.5, 8.5, 9\)? Wait, no, the original data after ordering: positions 1 - 19. Median is position 10. Lower half: positions 1 - 9, upper half: positions 11 - 19. So upper half data: \(7, 7.5, 7.5, 8, 8, 8.5, 8.5, 9\)? Wait, no, the \(11^{\text{th}}\) value is \(7\)? Wait, no, let's re - list the ordered data with positions:

1: \(4.5\)

2: \(5\)

3: \(5\)

4: \(5\)

5: \(6\)

6: \(6\)

7: \(6\)

8: \(6\)

9: \(7\)

10: \(7\) (median)

11: \(7\)

12: \(7\)

13: \(7.5\)

14: \(7.5\)

15: \(8\)

16: \(8\)

17: \(8.5\)

18: \(8.5\)

19: \(9\)

Ah, I made a mistake earlier. The lower half is positions 1 - 9: \(4.5,5,5,5,6,6,6,6,7\) (9 values). The upper half is positions 11 - 19: \(7,7,7.5,7.5,8,8,8.5,8.5,9\) (9 values). Now, the median of the upper half (Q3) is the \(\frac{9 + 1}{2}=5^{\text{th}}\) value in the upper half. The upper half data ordered (it's already ordered): positions 1 (of upper half): \(7\), 2: \(7\), 3: \(7.5\), 4: \(7.5\), 5: \(8\). So Q3 is \(8\).

Step6: Find Max

The maximum value (Max) is the largest number in the data set. Looking at the ordered data, the largest number is \(9\).

Answer:

Blank 1 (Min): \(4.5\)

Blank 2 (Q1): \(6\)

Blank 3 (Median): \(7\)

Blank 4 (Q3): \(8\)

Blank 5 (Max): \(9\)