Mean

1. Child: Let’s say you and your friends have some apples. To find out how many apples you each have on average, or the ‘mean’, you add up all your apples and then divide by the number of people. So if there are 3 of you and you have 9 apples altogether, you each have 9 divided by 3, or 3 apples on average!

2. Teenager: The ‘mean’ is just a fancy word for average. Imagine if you’ve scored different points in a video game over several rounds. To find your average or ‘mean’ score, you’d add up all your scores, then divide by the number of rounds you played. This gives you a good idea of your typical score.

3. Undergrad majoring in the same subject: The mean, or arithmetic mean, is a measure of central tendency in statistics. You calculate it by summing all the values in a data set and then dividing by the number of values. It provides a measure of the ‘central’ or ’typical’ value. However, it can be influenced by outliers or extreme values, which makes other measures like the median or mode important too.

4. Grad student: The mean is one of the fundamental measures in statistics, often serving as a key indicator of central tendency. Its calculation involves summing all observations in a dataset and dividing by the count of observations. While it’s widely used due to its mathematical properties, it’s also sensitive to extreme values or outliers. Therefore, understanding its limitations is crucial, particularly when dealing with skewed distributions.

5. Colleague (Fellow Researcher/Engineer): The arithmetic mean, one of the key pillars in descriptive statistics and inferential methods, provides an average measure across a dataset by summing all observations and dividing by the sample size. It’s the basis for numerous statistical methods, including variance, standard deviation, and correlation. However, its sensitivity to outliers and skewed distributions requires careful interpretation and sometimes preferential use of other measures like the median or the geometric mean, particularly in the realm of skewed data or ratio scales.

The mean, commonly called the average, is the sum of all values divided by the number of values. It provides an central value representing the data.

For a dataset X with values x1, x2, …, xn, the mean is:

(x1 + x2 + … + xn) / n

Java example:

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double mean(int[] nums) {
  int sum = 0;
  for (int x : nums) {
    sum += x;
  }
  return (double) sum / nums.length;
}

C++ example:

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double mean(const vector<int>& nums) {
  int sum = 0;
  for (int x : nums) {
    sum += x;
  }
  return static_cast<double>(sum) / nums.size();
}

Python example:

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from statistics import mean

def data_mean(nums):
  return mean(nums)

# Or manually
def manual_mean(nums):
  sum = 0
  for x in nums:
    sum += x
  return sum / len(nums)  

The mean gives a sense of the “center” of the data and is the balance point if one were to redistribute weight. It is sensitive to outliers compared to the median.