Question 1176654: raw scores of 48 students in a mathematics 8 test
scores: f: lb: cumulative frequency cf:
46-50| 1 |45.5 | 48 |
41-45| 5 |40.5 | 47 |
36-40| 11 |35.5 | 42 |
31-35| 12 |30.5 | 31 |
26-30| 11 |25.5 | 19 |
21-25| 5 |20.5 | 8 |
16-20| 2 |15.5 | 3 |
11-15| 1 |10.5 | 1 |
| |Σr=48 | | |
please help me with this thank you so much
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's find the quartiles for the given grouped data.
**1. Understanding Quartiles**
* **Q1 (First Quartile):** The value below which 25% of the data falls.
* **Q2 (Second Quartile):** The median, the value below which 50% of the data falls.
* **Q3 (Third Quartile):** The value below which 75% of the data falls.
**2. Formulas for Grouped Data**
The formula for finding quartiles in grouped data is:
* Qk = L + [(kN/4 - cf) / f] * w
Where:
* Qk = the kth quartile
* L = lower boundary of the quartile class
* N = total number of data points
* cf = cumulative frequency of the class before the quartile class
* f = frequency of the quartile class
* w = class width
**3. Calculate Quartiles**
* N = 48
* Class width (w) = 5 (e.g., 50 - 46 + 1 = 5)
**a) Q1 (First Quartile)**
* kN/4 = (1 * 48) / 4 = 12
* The 12th value falls in the 26-30 class (cf = 19, which is > 12).
* L = 25.5
* cf = 8
* f = 11
* Q1 = 25.5 + [(12 - 8) / 11] * 5
* Q1 = 25.5 + (4 / 11) * 5
* Q1 = 25.5 + 20 / 11
* Q1 = 25.5 + 1.818
* Q1 ≈ 27.32
**b) Q2 (Second Quartile)**
* kN/4 = (2 * 48) / 4 = 24
* The 24th value falls in the 31-35 class (cf = 31, which is > 24).
* L = 30.5
* cf = 19
* f = 12
* Q2 = 30.5 + [(24 - 19) / 12] * 5
* Q2 = 30.5 + (5 / 12) * 5
* Q2 = 30.5 + 25 / 12
* Q2 = 30.5 + 2.083
* Q2 ≈ 32.58
**c) Q3 (Third Quartile)**
* kN/4 = (3 * 48) / 4 = 36
* The 36th value falls in the 36-40 class (cf = 42, which is > 36).
* L = 35.5
* cf = 31
* f = 11
* Q3 = 35.5 + [(36 - 31) / 11] * 5
* Q3 = 35.5 + (5 / 11) * 5
* Q3 = 35.5 + 25 / 11
* Q3 = 35.5 + 2.273
* Q3 ≈ 37.77
**Summary**
* Q1 ≈ 27.32
* Q2 ≈ 32.58
* Q3 ≈ 37.77
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