a) The minimum data value is 430, the first quartile is 650, the median is 702, the third quartile is 800, and the maximum is 853.
b) The range is 423, and the interquartile range is 150.
The measures of central tendency are the typical or central values that values give us a good summary of the distribution of data.
When the data is arranged in ascending order: 430, 619, 645, 650, 690, 700, 704, 725, 730, 760, 800, 850, 852, 853, we can determine most of the measures of central tendency as follows:
a) Minimum = 430
First Quartile (Q1): This is the median of the first half of the data. There are 14 data points, the first half is the first 7 values.
Thus, the median of the first half of 430, 619, 645, 650, 690, 700, and 704 is 650.
Median (Q2): This is the middle value of the data. There are 14 data points, the median is the average of the 7th and 8th values, which are 700 and 704.
Thus, the median is (700 + 704) / 2 = 702.
The third quartile (Q3) represents the median of the second half of the data. The second half is the last 7 numbers.
Thus, the median of 725, 730, 760, 800, 850, 852, 853 is 800.
The Maximum = 853
The Range is the difference between the maximum and minimum values in the data. The range is 853 - 430 = 423.
Interquartile Range (IQR): This is the range of the middle 50% of the data, or in other words, Q3 - Q1. The IQR is 800 - 650 = 150.
Thus, we can conclude that the minimum is 430, the first quartile is 650, the median is 702, the third quartile is 800, the maximum is 853, the range is 423, and the interquartile range is 150.