Answer :
To solve this problem, we will follow systematic steps to find the representation in discrete series table, mean, median, mode, and the quartiles.
1. Represent in Discrete Series Table:
The discrete series table will list each unique weight and its frequency, i.e., how many times each weight appears in the dataset.
[tex]\[ \begin{array}{|c|c|} \hline \text{Weight (kg)} & \text{Frequency} \\ \hline 0.655 & 1 \\ 2 & 1 \\ 25 & 7 \\ 27 & 8 \\ 29 & 9 \\ 35 & 8 \\ 38 & 5 \\ 40 & 6 \\ 48 & 1 \\ 110 & 1 \\ \hline \end{array} \][/tex]
2. Mean (x):
Mean is calculated by dividing the sum of all weights by the number of weights.
Given the data, the Mean (x) is:
[tex]\[ x = 32.3969185619956 \][/tex]
3. Median (Md):
The median is the middle value of the dataset when arranged in ascending order. For an even number of observations, it is the average of the two central values.
Given the data, the Median (Md) is:
[tex]\[ \text{Md} = 29.0 \][/tex]
4. Mode (mo):
The mode is the value that appears most frequently in the dataset.
Given the data, the Mode (mo) is:
[tex]\[ \text{mo} = 29 \][/tex]
5. Upper Quartile (Q3):
The upper quartile (Q3) is the median of the upper half of the dataset. It is the 75th percentile.
Given the data, the Upper Quartile (Q3) is:
[tex]\[ Q3 = 38.0 \][/tex]
6. Lower Quartile (Q1):
The lower quartile (Q1) is the median of the lower half of the dataset. It is the 25th percentile.
Given the data, the Lower Quartile (Q1) is:
[tex]\[ Q1 = 27.0 \][/tex]
By following these steps, we have calculated the necessary statistics for the given dataset.
1. Represent in Discrete Series Table:
The discrete series table will list each unique weight and its frequency, i.e., how many times each weight appears in the dataset.
[tex]\[ \begin{array}{|c|c|} \hline \text{Weight (kg)} & \text{Frequency} \\ \hline 0.655 & 1 \\ 2 & 1 \\ 25 & 7 \\ 27 & 8 \\ 29 & 9 \\ 35 & 8 \\ 38 & 5 \\ 40 & 6 \\ 48 & 1 \\ 110 & 1 \\ \hline \end{array} \][/tex]
2. Mean (x):
Mean is calculated by dividing the sum of all weights by the number of weights.
Given the data, the Mean (x) is:
[tex]\[ x = 32.3969185619956 \][/tex]
3. Median (Md):
The median is the middle value of the dataset when arranged in ascending order. For an even number of observations, it is the average of the two central values.
Given the data, the Median (Md) is:
[tex]\[ \text{Md} = 29.0 \][/tex]
4. Mode (mo):
The mode is the value that appears most frequently in the dataset.
Given the data, the Mode (mo) is:
[tex]\[ \text{mo} = 29 \][/tex]
5. Upper Quartile (Q3):
The upper quartile (Q3) is the median of the upper half of the dataset. It is the 75th percentile.
Given the data, the Upper Quartile (Q3) is:
[tex]\[ Q3 = 38.0 \][/tex]
6. Lower Quartile (Q1):
The lower quartile (Q1) is the median of the lower half of the dataset. It is the 25th percentile.
Given the data, the Lower Quartile (Q1) is:
[tex]\[ Q1 = 27.0 \][/tex]
By following these steps, we have calculated the necessary statistics for the given dataset.
