2.2 Two Grade 11 Mathematics classes have the same number of learners. The five- number summaries of the marks obtained by these classes for a test are shown below. CLASS A $$ (30 ; 48 ; 65 ; 82 ; 90) $$ CLASS B $$ (50 ; 58 ; 65 ; 75 ; 90) $$ The parents of learners in CLASS A and CLASS B observe that both classes have the same median and the same maximum mark and therefore claim that there is no difference in the performance between these classes. Do you agree with this claim? Use at least Two different arguments to justify your answer. [13]

Question

UpStudy AI · Accepted Answer

**Argument 1: Differences in Spread (Range and Interquartile Range)**

For Class A, the five-number summary is  
$$
(30;\ 48;\ 65;\ 82;\ 90)
$$  
For Class B, the five-number summary is  
$$
(50;\ 58;\ 65;\ 75;\ 90)
$$

- **Range:**  
  The range is calculated as the difference between the maximum and minimum.  
  - Class A: $$ 90 - 30 = 60 $$  
  - Class B: $$ 90 - 50 = 40 $$  
  This shows that Class A has a wider spread of marks, indicating that while some students performed very well, others performed significantly lower than the rest of the class, which affects the overall performance distribution.

- **Interquartile Range (IQR):**  
  The IQR is calculated as the difference between the third quartile and the first quartile.  
  - Class A: $$ 82 - 48 = 34 $$  
  - Class B: $$ 75 - 58 = 17 $$  
  A larger IQR in Class A means the middle 50% of its learners’ marks are more spread out compared to Class B. Even though the medians are the same, a wider IQR indicates greater variability in performance in Class A.

---

**Argument 2: Distribution Shape and Performance Consistency**

- **Lower and Upper Sections of the Distribution:**  
  For Class A, the minimum mark is $$30$$ compared to Class B's minimum of $$50$$. This suggests that Class A has some learners with very low marks that pull the distribution downward, even though the maximum mark is the same in both classes ($$90$$).  
  
- **Implications for Performance:**  
  The data indicate that while both classes have a median of $$65$$ and an equal maximum, Class B has a more concentrated distribution of marks (i.e., less variability) with both the lower and upper quartiles being closer together. This consistency suggests that most of the learners in Class B performed closer together around the median. In contrast, Class A's larger spread shows a more diverse performance, which might require additional attention for lower-performing students despite a similar median.

---

**Conclusion:**

The claim that there is no difference in performance between the classes is not justified because the contexts provided by the five-number summaries reveal differences in the spread and concentration of scores. The two arguments above, based on the differences in the range/IQR and the differences in distribution shape, clearly indicate that the overall performance profiles of Class A and Class B are not the same.
There are differences in how the marks are spread between Class A and Class B. While both classes have the same median and maximum mark, Class A has a wider range and a larger interquartile range, meaning some students performed much better or worse than others. Class B has a more consistent distribution of marks. Therefore, the classes do not perform the same overall.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Statistics Questions