Use the following data set to answer this question:
14, 17, 13, 15, 14, 19, 2, 18
What is the lower quartile?
*
13
13.5
14
14.5
To find the lower quartile in a dataset, the data must first be arranged in ascending order:
2, 13, 14, 14, 15, 17, 18, 19
The data set has 8 numbers, so to find the lower quartile, we need to find the median of the first half of the data set. Since 8 is an even number, the first half consists of the first four numbers. The median of this half is the average of the two middle numbers.
2, 13, 14, 14
The two middle numbers are 13 and 14.
(13 + 14) / 2 = 27 / 2 = 13.5
Therefore, the lower quartile is 13.5.
To find the lower quartile, you need to organize the data set in ascending order (from lowest to highest). The given data set is:
2, 13, 14, 14, 15, 17, 18, 19
The lower quartile divides the data into four equal parts. To calculate it, you need to find the median of the lower half of the data set. In this case, the lower half consists of the first four numbers:
2, 13, 14, 14
Since there is an even number of data points, the median is found by averaging the middle two values. In this case, the two middle values are 13 and 14. So the lower quartile, also known as the first quartile (Q1), is:
(Q1) = (13 + 14) / 2 = 27 / 2 = 13.5
Therefore, the lower quartile is 13.5.
To find the lower quartile, we first need to arrange the data set in ascending order:
2, 13, 14, 14, 15, 17, 18, 19
Next, we calculate the position of the lower quartile in the data set. The formula to find the position is given by (n+1)/4, where n is the number of data points in the set:
(8+1)/4 = 2.25
Since 2.25 is not a whole number, we take the average of the values in positions 2 and 3:
(13 + 14)/2 = 13.5
Therefore, the lower quartile of the given data set is 13.5.