Given the data set {15; 3; 26; 3; 1; 0; 8; 7; 4; 9}, determine the following:
1. the mode
2. the mean
3. the median
4. the range
5. the upper quartile
1. The mode is 3 because it appears twice, more than any other number in the data set.
2. To find the mean, add up all the numbers in the data set and then divide by the total number of numbers.
(15 + 3 + 26 + 3 + 1 + 0 + 8 + 7 + 4 + 9)/10 = 76/10 = 7.6
The mean is 7.6.
3. To find the median, first arrange the numbers in ascending order: 0, 1, 3, 3, 4, 7, 8, 9, 15, 26.
Since there are 10 numbers, the middle value is the (10/2)th value and the (10/2 + 1)th value.
The 5th value is 4 and the 6th value is 7.
Therefore, the median is (4 + 7)/2 = 11/2 = 5.5.
4. The range is the difference between the largest and smallest numbers in the data set.
The largest number is 26 and the smallest number is 0.
Therefore, the range is 26 - 0 = 26.
5. The upper quartile is the median of the upper half of the data set.
Since there are 10 numbers, the upper half consists of the 6th, 7th, 8th, 9th, and 10th values.
The 7th value is 8 and the 8th value is 9.
Therefore, the upper quartile is (8 + 9)/2 = 17/2 = 8.5.