In the data set below, what are the lower quartile, the median, and the upper quartile?
1 3 4 4 5 6 7 7 78 8
lower quartile =
median =
upper quartile =
To find the lower quartile, median, and upper quartile in a dataset, you first need to arrange the data in ascending order:
1 3 4 4 5 6 7 7 8 78
Now, the lower quartile (Q1) is the median of the lower half of the data set. Since there are 10 data points, the lower half consists of the first 5 data points. Therefore, Q1 = (4 + 4) / 2 = 4.
Next, the median (Q2) is the middle value of the data set, which in this case is the 5th value. Therefore, Q2 = 5.
Finally, the upper quartile (Q3) is the median of the upper half of the data set. The upper half consists of the last 5 data points. Therefore, Q3 = (7 + 7) / 2 = 7.
Therefore, in the given data set, the lower quartile is 4, the median is 5, and the upper quartile is 7.