A set of data consists of five numbers.The mode is 2.The median is 3.The mean is 4. The difference between the largest and smallest number is 6.What are the five numbers?
Answer (1)
Answer:Here's how we can solve this problem step-by-step: 1. Understand the terms: - Mode: The number that appears most frequently in a data set. We know the mode is 2, so 2 must appear at least twice.- Median: The middle number when the data is ordered. Since there are five numbers, the median is the third number. We know the median is 3.- Mean: The average of the numbers. We know the mean is 4. The sum of the five numbers is therefore 4 * 5 = 20.- Range: The difference between the largest and smallest numbers. We know the range is 6. 2. Deduce the numbers: Let's represent the five numbers in ascending order as a, b, c, d, e. - We know that c = 3 (median).- We know that a and b are 2 (mode).- The sum of the numbers is a + b + c + d + e = 20.- Substituting what we know, we get 2 + 2 + 3 + d + e = 20. This simplifies to d + e = 13.- We also know that e - a = 6 (range). Since a = 2, then e = 8. 3. Find the remaining number: - Since d + e = 13, and e = 8, then d = 13 - 8 = 5. 4. The five numbers: Therefore, the five numbers are 2, 2, 3, 5, 8.
