Question 1185332: 1. A random sample of 9 airline carry-on luggage bags have the weights: 12, 25, 10 ,38, 12, 19, 8, 12, 17.
Find the measures of center: Mean, median, mode, midrange.
NEED HELP WITH 2 QUESTIONS!!!
2.A sample of 7 northern pikes from Taltson Lake have the lengths: 21, 27, 46, 35, 41, 36, 25.
Find the measures of variation: Range, standard deviation, and variance
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **1. Carry-on Luggage Weights:**
* **Mean:** Sum of weights / Number of bags = (12 + 25 + 10 + 38 + 12 + 19 + 8 + 12 + 17) / 9 = 173 / 9 ≈ 19.22
* **Median:** First, order the weights from least to greatest: 8, 10, 12, 12, 12, 17, 19, 25, 38. The median is the middle value, which is 12.
* **Mode:** The mode is the most frequent value. In this case, 12 appears 3 times, which is the most. So, the mode is 12.
* **Midrange:** (Maximum value + Minimum value) / 2 = (38 + 8) / 2 = 46 / 2 = 23
**2. Northern Pike Lengths:**
* **Range:** Maximum value - Minimum value = 46 - 21 = 25
* **Standard Deviation:**
1. **Calculate the mean:** (21 + 27 + 46 + 35 + 41 + 36 + 25) / 7 = 231 / 7 = 33
2. **Subtract the mean from each length and square the result:**
* (21 - 33)² = 144
* (27 - 33)² = 36
* (46 - 33)² = 169
* (35 - 33)² = 4
* (41 - 33)² = 64
* (36 - 33)² = 9
* (25 - 33)² = 64
3. **Sum the squared differences:** 144 + 36 + 169 + 4 + 64 + 9 + 64 = 490
4. **Divide the sum by (n - 1), where n is the number of lengths (this is the sample variance):** 490 / (7 - 1) = 490 / 6 ≈ 81.67
5. **Take the square root of the variance to get the standard deviation:** √81.67 ≈ 9.04
* **Variance:** As calculated in step 4 above, the variance is approximately 81.67.
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