Math Problem Statement

Find the median and mean of the data set below: 29, comma, 41, comma, 41, comma, 7, comma, 40, comma, 2, comma, 1 29,41,41,7,40,2,1

Solution

Let's find the mean and median of the data set:
Data: 29, 41, 41, 7, 40, 2, 1

Step 1: Find the Mean

The mean (average) is calculated as:
Mean=valuesnumber of values\text{Mean} = \frac{\sum \text{values}}{\text{number of values}}

Sum of values:
29+41+41+7+40+2+1=16129 + 41 + 41 + 7 + 40 + 2 + 1 = 161

Number of values:
77

Mean=161723\text{Mean} = \frac{161}{7} \approx 23

Step 2: Find the Median

The median is the middle value when the data is arranged in ascending order.

Sorted data: 1, 2, 7, 29, 40, 41, 41

Since we have 7 numbers (odd count), the median is the 4th value:
Median=29\text{Median} = 29

Final Answer:

  • Mean23
  • Median = 29

Would you like a more detailed breakdown? Let me know if you have questions!


Related Questions:

  1. What happens if there are an even number of values when finding the median?
  2. How does an outlier affect the mean and median?
  3. What is the mode of this data set?
  4. How can we calculate the range of this data set?
  5. How would adding another 41 change the mean and median?

Tip:

The median is less sensitive to extreme values (outliers) than the mean, making it a better measure of central tendency for skewed data!

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Math Problem Analysis

Mathematical Concepts

Statistics
Mean
Median
Data Analysis

Formulas

Mean = (Sum of values) / (Number of values)
Median = Middle value of the sorted data set

Theorems

Definition of Mean
Definition of Median

Suitable Grade Level

Grades 6-8