Answer:
Explanation:
To construct the data set, we need to consider the given measures of central tendency:
Mean: 9
Median: 8
Mode: 5
Midrange: 11.5
We can start by finding five values that are less than or equal to the median of 8, and five values that are greater than or equal to the median. Since the mode is 5, we can include it as one of the lower values.
Let's try to find the other four lower values that satisfy the given conditions:
The sum of all values is 10 * 9 = 90 (since there are 10 values and the mean is 9).
The mode is 5, so we need at least two values that are equal to 5.
The midrange is (max + min) / 2 = 11.5, so we need a maximum value that is 3 more than the minimum value.
Here's one possible set of 10 values that satisfy these conditions, listed in ascending order:
{2, 3, 4, 5, 5, 8, 9, 10, 12, 13}
To check that this set of values satisfies the given conditions:
The mean is (2+3+4+5+5+8+9+10+12+13) / 10 = 9.
The median is 8 (the middle value when the values are listed in ascending order).
The mode is 5 (the most common value).
The midrange is (13 + 2) / 2 = 7.5 + 4 = 11.5 (the average of the maximum and minimum values).