Question 1171481: x Freq
100 11
90 2
70 6
50 6
mean =
median =
mode =
sample variance =
sample standard deviation =
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Let's calculate the mean, median, mode, sample variance, and sample standard deviation for the given data.
**1. Mean:**
* **Sum of (x * Freq):**
* (100 * 11) + (90 * 2) + (70 * 6) + (50 * 6) = 1100 + 180 + 420 + 300 = 2000
* **Total Frequency (n):**
* 11 + 2 + 6 + 6 = 25
* **Mean (x̄):**
* 2000 / 25 = 80
**2. Median:**
* Since there are 25 data points, the median is the (25 + 1) / 2 = 13th value.
* Let's list the values in order:
* 100 (11 times)
* 90 (2 times)
* 70 (6 times)
* 50 (6 times)
* The 13th value falls within the 70's.
* Therefore, the median is 70.
**3. Mode:**
* The mode is the value that appears most frequently.
* 100 appears 11 times, which is the highest frequency.
* Therefore, the mode is 100.
**4. Sample Variance (s²):**
* **Calculate (x - x̄)² * Freq:**
* (100 - 80)² * 11 = 20² * 11 = 400 * 11 = 4400
* (90 - 80)² * 2 = 10² * 2 = 100 * 2 = 200
* (70 - 80)² * 6 = (-10)² * 6 = 100 * 6 = 600
* (50 - 80)² * 6 = (-30)² * 6 = 900 * 6 = 5400
* **Sum of (x - x̄)² * Freq:**
* 4400 + 200 + 600 + 5400 = 10600
* **Sample Variance (s²):**
* 10600 / (25 - 1) = 10600 / 24 ≈ 441.67
**5. Sample Standard Deviation (s):**
* **Sample Standard Deviation (s):**
* √s² = √441.67 ≈ 21.02
**Summary:**
* Mean = 80
* Median = 70
* Mode = 100
* Sample Variance ≈ 441.67
* Sample Standard Deviation ≈ 21.02
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