Determine the possible ages of a family of five based on the following information:

Question

[ /3 marks]

Mode : 41 Median: 10 Mean: 20

Answer 1

To determine the possible ages of a family of five based on the given information, we can use the following equations:

1) Mode: The mode is the value that appears most frequently in the data set. In this case, the mode is 41, which means at least one member of the family must be 41 years old.

2) Median: The median is the middle value of a data set when ordered from least to greatest. In this case, the median is 10. Since there are five members in the family, the second and third members must have ages that average to 10. Let's call the second member's age x and the third member's age y. Therefore, we can write the equation (x + y) / 2 = 10.

3) Mean: The mean is the average of all the values in the data set. In this case, the mean is 20. Since there are five members in the family, the sum of all their ages must be 5 * 20 = 100. Let's call the remaining two members' ages as a and b. Therefore, we can write the equation a + b + 41 + x + y = 100.

Combining these equations, we have:

(x + y) / 2 = 10 --> x + y = 20 (equation 1)
a + b + 41 + x + y = 100 --> a + b + x + y = 59 (equation 2)

From equation 1, we know that x + y = 20. Substituting this into equation 2, we have:

a + b + 20 = 59 --> a + b = 39 (equation 3)

Now, we need to find possible values for a and b that satisfy equation 3. Since we cannot determine the exact values of a and b based on the given information, there are multiple possible solutions. Here are a few examples:

- a = 1, b = 38
- a = 2, b = 37
- a = 3, b = 36
- a = 4, b = 35
- and so on...

Therefore, the possible ages of the family members could be:

41, x, y, a, b

where x + y = 20, and a + b = 39.