A set of 10 numbers has a mean of 32. What would happen to the measures of central tendency if each of the 10 numbers were decreased by 5? Discuss all the measures of central tendency.
To understand the impact of decreasing each of the 10 numbers in a set by 5 on the measures of central tendency, we need to consider three key measures: mean, median, and mode.
1. Mean: The mean is calculated by summing up all the numbers in the set and dividing it by the total count of numbers. To determine the new mean after decreasing each number by 5, we subtract 5 from each number, calculate the new sum, and divide it by the total count.
- Suppose the original set of 10 numbers had a mean of 32. If we decrease each number by 5, the new set would have a mean of 27 because each number contributes 5 less to the sum.
2. Median: The median is the middle value in an ordered set of numbers. To determine the impact on the median after decreasing each number by 5, we need to examine the relative positions of the numbers and their relationship to the median.
- If the original set had an odd number of values, the median wouldn't change because the relative order of the numbers remains the same.
- If the original set had an even number of values, the median could change. However, since each number is decreased by the same value (5), the relative order of the numbers will not be affected. Therefore, the median would remain the same.
3. Mode: The mode is the most frequently occurring value in a set. Since we're only decreasing each number by 5, the number that occurs most frequently in the original set will still be the mode after the decrease. Therefore, the mode would remain the same.
In summary, if each of the 10 numbers in a set with a mean of 32 is decreased by 5:
- The mean would decrease by 5 and become 27.
- The median would either remain the same or stay unaffected.
- The mode would remain the same.