SOLUTION: Use the appropriate formula to find the mean,The madian,and the mode of each grouped data. scores: Frequency: 46-50. 2 41-45.

Algebra ->  Probability-and-statistics -> SOLUTION: Use the appropriate formula to find the mean,The madian,and the mode of each grouped data. scores: Frequency: 46-50. 2 41-45.       Log On


   

Question 1176041: Use the appropriate formula to find the mean,The madian,and the mode of each grouped data.
scores: Frequency:
46-50. 2
41-45. 9
36-40. 10
31-35. 14
26-30. 10
21-25. 5
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
**1. Calculate the Midpoints**
* Find the midpoint of each class interval:
* 46-50: (46 + 50) / 2 = 48
* 41-45: (41 + 45) / 2 = 43
* 36-40: (36 + 40) / 2 = 38
* 31-35: (31 + 35) / 2 = 33
* 26-30: (26 + 30) / 2 = 28
**2. Mean**
* Use the formula:
* Mean (x̄) = Σ(midpoint * frequency) / Σfrequency
* x̄ = [(48 * 2) + (43 * 9) + (38 * 10) + (33 * 14) + (28 * 10)] / (2 + 9 + 10 + 14 + 10)
* x̄ = (96 + 387 + 380 + 462 + 280) / 45
* x̄ = 1605 / 45
* x̄ ≈ 35.67
**3. Median**
1. **Find the Cumulative Frequencies:**
* 46-50: 2
* 41-45: 2 + 9 = 11
* 36-40: 11 + 10 = 21
* 31-35: 21 + 14 = 35
* 26-30: 35 + 10 = 45
2. **Identify the Median Class:**
* The total number of scores (N) is 45.
* The median class is the class where the cumulative frequency is greater than or equal to N/2 (which is 22.5 in this case).
* The median class is 31-35.
3. **Calculate the Median:**
* Use the formula:
* Median = L + [(N/2 - cf) / f] * w
* Where:
* L = Lower boundary of the median class (30.5)
* N = Total number of scores (45)
* cf = Cumulative frequency of the class before the median class (21)
* f = Frequency of the median class (14)
* w = Class width (5)
* Median = 30.5 + [(22.5 - 21) / 14] * 5
* Median = 30.5 + (1.5 / 14) * 5
* Median ≈ 31.04
**4. Mode**
* The modal class is the class with the highest frequency.
* In this case, the modal class is 31-35.
**Summary**
* Mean: 35.67
* Median: 31.04
* Mode: 31-35