Sure, let's break down the solution step by step for the given questions.
### Question 3: Median Calculation
#### Morning (AM) Group
The morning group data given in the tabular format can be expanded and ordered as follows:
[tex]\[ [30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59] \][/tex]
To find the median:
1. Arrange the numbers in ascending order (already done above).
2. Identify the middle number(s). For 21 data points:
- The middle position is at [tex]\(\left(\frac{21+1}{2}\right) = 11\)[/tex].
- So, the 11th data point is 49.
Therefore, the median of the morning (AM) group is:
[tex]\[ \text{Median (AM)} = 49.0 \][/tex]
#### Afternoon (PM) Group
The afternoon group only has one data point:
[tex]\[ [49] \][/tex]
Since there is only one data point, that point is the median.
Therefore, the median of the afternoon (PM) group is:
[tex]\[ \text{Median (PM)} = 49.0 \][/tex]
### Question 4: First Quartile (Q1) Calculation
#### Morning (AM) Group
The first quartile (Q1) is the median of the first half of the data not including the overall median value. For the morning group of 21 data points, the first half includes the first 10 data points:
[tex]\[ [30, 31, 32, 33, 34, 35, 36, 37, 38, 39] \][/tex]
To find Q1:
1. Arrange the numbers in ascending order (already done above).
2. The median of these 10 data points is at [tex]\(\left(\frac{10+1}{2}\right) = 5.5\)[/tex]. This involves taking the average of the 5th and 6th data points.
3. The 5th and 6th data points are 34 and 36.
[tex]\[ Q1 = \frac{34 + 36}{2} = 35.0 \][/tex]
Therefore, the first quartile (Q1) of the morning (AM) group is:
[tex]\[ Q1 \text{ (AM)} = 35.0 \][/tex]
#### Afternoon (PM) Group
Since the afternoon group only has one data point [tex]\([49]\)[/tex], the first quartile (Q1) in this case is also that single data point.
Therefore, the first quartile (Q1) of the afternoon (PM) group is:
[tex]\[ Q1 \text{ (PM)} = 49.0 \][/tex]
In summary:
1. [tex]\(\text{Median (AM)} = 49.0\)[/tex]
2. [tex]\(\text{Median (PM)} = 49.0\)[/tex]
3. [tex]\(\text{Q1 (AM)} = 35.0\)[/tex]
4. [tex]\(\text{Q1 (PM)} = 49.0\)[/tex]
