Question 1171480: x Freq
1 4
2 2
3 4
6 10
mean =
median =
mode =
sample variance =
sample standard deviation =
Answer by CPhill(1959)   (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):** * (1 * 4) + (2 * 2) + (3 * 4) + (6 * 10) = 4 + 4 + 12 + 60 = 80
* **Total Frequency (n):** * 4 + 2 + 4 + 10 = 20
* **Mean (x̄):** * 80 / 20 = 4
**2. Median:**
* Since there are 20 data points, the median is the average of the 10th and 11th values.
* Let's list the values in order:
* 1 (4 times)
* 2 (2 times)
* 3 (4 times)
* 6 (10 times)
* The 10th and 11th values are both 6.
* Therefore, the median is 6.
**3. Mode:**
* The mode is the value that appears most frequently.
* 6 appears 10 times, which is the highest frequency.
* Therefore, the mode is 6.
**4. Sample Variance (s²):**
* **Calculate (x - x̄)² * Freq:**
* (1 - 4)² * 4 = (-3)² * 4 = 9 * 4 = 36
* (2 - 4)² * 2 = (-2)² * 2 = 4 * 2 = 8
* (3 - 4)² * 4 = (-1)² * 4 = 1 * 4 = 4
* (6 - 4)² * 10 = (2)² * 10 = 4 * 10 = 40
* **Sum of (x - x̄)² * Freq:**
* 36 + 8 + 4 + 40 = 88
* **Sample Variance (s²):**
* 88 / (20 - 1) = 88 / 19 ≈ 4.63
**5. Sample Standard Deviation (s):**
* **Sample Standard Deviation (s):**
* √s² = √4.63 ≈ 2.15
**Summary:**
* Mean = 4
* Median = 6
* Mode = 6
* Sample Variance ≈ 4.63
* Sample Standard Deviation ≈ 2.15
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