Question
Find the mean, median, and mode of the set of numbers. \( 95,76,98,76,53,52,95,59,73,62,53,53 \) What is the mean? 70.4 (Type an integer or decimal rounded to one decimal place as needed.) What is the median? (Type an integer or a decimal.)
Ask by Guzman Gross. in the United States
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
**Mean:** 70.4
**Median:** 67.5
Solution
**Mean: 70.4**
**Median: 67.5**
**Detailed Calculation:**
1. **Mean:**
- **Sum of all numbers:**
\( 95 + 76 + 98 + 76 + 53 + 52 + 95 + 59 + 73 + 62 + 53 + 53 = 845 \)
- **Number of data points:** 12
- **Mean:**
\( \frac{845}{12} = 70.4167 \)
Rounded to one decimal place: **70.4**
2. **Median:**
- **Sorted List:** 52, 53, 53, 53, 59, 62, 73, 76, 76, 95, 95, 98
- **Number of data points:** 12 (even)
- **Median Position:** Average of the 6th and 7th numbers.
- 6th number: 62
- 7th number: 73
- **Median:**
\( \frac{62 + 73}{2} = \frac{135}{2} = 67.5 \)
3. **Mode (Bonus):**
- The number that appears most frequently is **53**, appearing three times.
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Simplify this solution Bonus Knowledge
To find the mean, you add all the numbers together and divide by the total count. The sum of your set of numbers \( 95 + 76 + 98 + 76 + 53 + 52 + 95 + 59 + 73 + 62 + 53 + 53 = 850 \). Since there are 12 numbers in total, the mean is \( \frac{850}{12} \approx 70.8 \). For the median, you need to order the numbers: \( 52, 53, 53, 53, 59, 62, 73, 76, 76, 95, 95, 98 \). With 12 numbers (an even amount), the median is the average of the 6th and 7th numbers, which are 62 and 73. Therefore, the median is \( \frac{62 + 73}{2} = 67.5 \).
