What is the third quartile of 45 + 48 + 48 + 57 + 58 + 68 + 68 + 76 + 79 + 84 + 86 + 88?
First, we need to put the numbers in order:
45, 48, 48, 57, 58, 68, 68, 76, 79, 84, 86, 88
The median of this data set is the middle number, or the average of the two middle numbers if there are an even number of values. Since there are 12 values in this data set, the median is the average of the 6th and 7th values:
median = (68 + 68) / 2 = 68
Next, we need to find the third quartile, which is the value that splits the upper 25% of the data set from the lower 75%. To do this, we first need to find the median of the upper half of the data set, which consists of:
76, 79, 84, 86, 88
The median of this data set is the average of the middle two values:
median = (84 + 86) / 2 = 85
Therefore, the third quartile is 85.