### Solutions:
#### 1.1.2 A learner that obtains a mark of 80% or more is said to have achieved a distinction. How many home-schooled Grade 12 learners achieved a distinction in Mathematical Literacy?
To determine the number of learners who achieved a distinction in Mathematical Literacy, we are given that a mark of 80% or more is required to achieve a distinction.
The number of home-schooled Grade 12 learners who achieved a distinction in Mathematical Literacy is 80.
#### 1.1.3 Find the difference between the values of the 2nd Quartiles in the above subject's results.
Quartiles divide a data set into four equal parts. The 2nd Quartile (Q2) is also known as the median, which is the middle value of the data set when it is ordered. The question asks for the difference between the medians of two subjects.
Given values:
- Median for Subject X: 50
- Median for Subject Y: 45
The difference between the 2nd Quartiles (medians) is:
[tex]\[ |50 - 45| = 5 \][/tex]
The difference between the 2nd Quartiles for the given subjects is 5.
#### 1.1.4 How many learners are represented by the inter-quartile range for Life Sciences?
The Inter Quartile Range (IQR) is the range between the first quartile (Q1, 25th percentile) and the third quartile (Q3, 75th percentile). The IQR gives us an idea about the spread of the middle 50% of the data.
Given:
- Q3 (Upper Quartile) = 80%
- Q1 (Lower Quartile) = 30%
The IQR is calculated as:
[tex]\[ 80 - 30 = 50 \][/tex]
The number of learners represented by the Inter Quartile Range (IQR) for Life Sciences is 50.
