Data Quartiles and Percentiles – Grade 12 CAPS Mathematical Literacy
Introduction
Understanding data quartiles and percentiles is crucial in analyzing and interpreting data distributions. These concepts help break down data into manageable sections, aiding in comparisons and identifying trends. This section aligns with the CAPS curriculum for Grade 12 Mathematical Literacy.
Key Points
 Quartiles:
 Quartiles divide data into four equal parts.
 First Quartile (Q1): 25th percentile.
 Second Quartile (Q2 or Median): 50th percentile.
 Third Quartile (Q3): 75th percentile.

Interquartile Range (IQR): Difference between Q3 and Q1, representing the middle 50% of the data.

Percentiles:
 Percentiles divide data into 100 equal parts.
 Helps identify the position of a value within a data set.

A percentile rank gives the percentage of data points below a particular value.

Formulas and Calculations:
 Median (Q2): Middle value of an ordered data set.
 Q1: Value at 25% of the ordered data.
 Q3: Value at 75% of the ordered data.
 Percentile Calculation:
[
P = \left(\frac{n \times k}{100}\right)^{th} \text{ value}
]
where ( n ) is the number of data points and ( k ) is the desired percentile.
RealWorld Applications
Example Problem:
A class of students received the following marks out of 100:
[ 45, 67, 89, 55, 48, 75, 92, 60, 70, 85 ]
StepbyStep Solution:
1. Order the data: 45, 48, 55, 60, 67, 70, 75, 85, 89, 92
2. Median (Q2): Middle value of ordered list
– If n = 10 (even), ( Q2 = \frac{(67+70)}{2} = 68.5 )
3. Calculate Q1 and Q3:
– ( Q1 ) is the median of the first half: 45, 48, 55, 60, 67
– ( Q1 = 55 )
– ( Q3 ) is the median of the second half: 70, 75, 85, 89, 92
– ( Q3 = 85 )
4. Interquartile Range (IQR):
– ( IQR = Q3 – Q1 = 85 – 55 = 30 )
Common Misconceptions and Errors
 Confusing Quartiles and Percentiles: Quartiles divide data into four equal parts, while percentiles divide it into 100 parts.
 Incorrect Ordering: Always arrange data in ascending order before calculating quartiles or percentiles.
 Overlooking Data Size: For an odd number of data points, directly pick the middle value for the median. For even numbers, average the two middle values.
Practice and Review
Sample Exam Questions:
1. Find Q1, Q2, and Q3 for the data set: 12, 15, 14, 10, 9, 20, 18, 17.
2. Determine the 40th percentile of the following marks: 23, 29, 35, 41, 47, 53, 59, 65, 71.
Solution Explanations:
1. Arrange the data set in ascending order: 9, 10, 12, 14, 15, 17, 18, 20.
– Q1: 11
– Median (Q2): 14.5
– Q3: 18
2. Percentile calculation:
– 40th percentile of 9 values: ( P = \frac{9 \times 40}{100} \approx 3.6 )
– [
\text{Interpolating} = (10 – 9) \times 0.6 + 9 = 9.6 \approx 10
]
Examination Tips:
– Look for keywords like “median,” “quartile,” and “percentile”.
– Verify your calculations by checking the position of the data points in the ordered set.
– Manage time effectively by organizing data clearly.
Connections and Extensions
 Connection to Probability: Percentiles are used in probability to determine cumulative distribution functions.
 RealWorld Implications: Understanding data distribution can aid in making predictive analyses in fields such as finance, health sciences, and social sciences.
Summary and Quick Review
 Median: Middle value in ordered data.
 Quartiles: Q1 (25th percentile), Q2 (50th percentile), Q3 (75th percentile).
 Percentile Rank: Position of a value within data divided into 100 parts.
Additional Resources
 Online Articles: Khan Academy’s Statistics and Probability section.
 Videos: YouTube channels like “Math Antics” and educational platforms such as Coursera.
By mastering quartiles and percentiles, you enhance your ability to understand and interpret data, which is an essential skill in many realworld situations【4:2†source】【4:3†source】.