In the data set below, what are the lower quartile, the median, and the upper quartile?
13445677788
lower quartile =
median =
upper quartile =
To find the lower quartile, median, and upper quartile in the given data set 13445677788, we first need to sort the data in ascending order:
1, 3, 4, 4, 5, 6, 7, 7, 8, 8
Now, we can identify the lower quartile, median, and upper quartile.
Lower quartile (Q1): The lower quartile is the median of the lower half of the data set. In this case, 1, 3, 4, 4, 5 have been assigned to the lower half of the data set. The median of this lower half is the average of the two middle values, which are 3 and 4. Therefore, the lower quartile (Q1) is 3.5.
Median: The median is the middle value of the data set, after sorting the data. In this case, the median is the average of the two middle values, which are 5 and 6. Therefore, the median is 5.5.
Upper quartile (Q3): The upper quartile is the median of the upper half of the data set. 6, 7, 7, 8, 8 have been assigned to the upper half of the data set. The median of this upper half is the average of the two middle values, which are 7 and 7. Therefore, the upper quartile (Q3) is 7.
In summary:
Lower quartile (Q1) = 3.5
Median = 5.5
Upper quartile (Q3) = 7