Points to Remember:

  • Calculating the median requires ordering the data.
  • The median is the middle value when data is ordered.
  • Removing a data point affects the median, especially with an odd number of data points.

Introduction:

This question requires a factual and analytical approach to determine the median pocket money among a group of friends and how the absence of one friend's contribution alters this median. The median, unlike the mean (average), is less sensitive to outliers; it represents the central tendency of the data. To calculate the median, we need the amount of pocket money each friend carries. Since this information is not provided, we will illustrate the process with hypothetical data.

Body:

1. Calculating the Median with 11 Friends:

Let's assume the following pocket money amounts (in dollars) for the 11 friends: 5, 7, 8, 10, 12, 15, 18, 20, 22, 25, 30.

To find the median:

  1. Order the data: 5, 7, 8, 10, 12, 15, 18, 20, 22, 25, 30
  2. Identify the middle value: Since there are 11 data points (an odd number), the median is the 6th value.

Therefore, the median pocket money is $15.

2. Calculating the Median with 10 Friends:

Now, let's assume one friend forgets their purse (let's remove the $30). The new data set is: 5, 7, 8, 10, 12, 15, 18, 20, 22, 25.

To find the new median:

  1. Order the data (already ordered): 5, 7, 8, 10, 12, 15, 18, 20, 22, 25
  2. Identify the middle value: Since there are 10 data points (an even number), the median is the average of the 5th and 6th values.

The median is (12 + 15) / 2 = $13.50.

3. Analysis of the Change:

The removal of the highest value ($30) resulted in a decrease in the median from $15 to $13.50. This demonstrates that the median, while less sensitive to outliers than the mean, is still affected by changes in the dataset, particularly when the number of data points is small and the removed value is significantly different from others. If the removed value was closer to the median, the change would be less significant.

Conclusion:

The median pocket money for the 11 friends, using our hypothetical data, was $15. When one friend forgot their purse, the median decreased to $13.50. This illustrates how the removal of a data point, even without knowing the exact values, can alter the median, especially with a small dataset. The impact of removing a data point depends on its value relative to the other values in the dataset. Further analysis would require the actual pocket money amounts of each friend. A more robust analysis might involve considering the distribution of pocket money and using statistical methods to account for potential uncertainties. Understanding central tendencies like the median is crucial for making informed decisions based on financial data.