Complete the five-number summary for the data set: 5, 2, 1, 3, 3, 6, 4, 2, 7.
To complete the five-number summary for the given data set, we need to find the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
To find the minimum, we simply need to identify the lowest value in the data set. In this case, the minimum is 1.
To find the maximum, we identify the highest value in the data set. In this case, the maximum is 7.
To find the median (Q2), we first arrange the data set in ascending order: 1, 2, 2, 3, 3, 4, 5, 6, 7. Then, we find the middle value. Since the data set has an odd number of values (9 in total), the median is the value in the middle position, which is 3.
To find the first quartile (Q1), we divide the data set into two halves. We take the lower half (1, 2, 2, 3) and arrange it in ascending order: 1, 2, 2, 3. Then, we find the median of this lower half. Since this subset has an even number of values (4 in total), we take the average of the two middle values. The two middle values are 1 and 2, so their average is (1 + 2) / 2 = 1.5. Therefore, the first quartile (Q1) is 1.5.
To find the third quartile (Q3), we take the upper half of the data set (3, 3, 4, 5, 6, 7) and arrange it in ascending order: 3, 3, 4, 5, 6, 7. We find the median of this upper half. Since this subset has an even number of values (6 in total), we take the average of the two middle values. The two middle values are 4 and 5, so their average is (4 + 5) / 2 = 4.5. Therefore, the third quartile (Q3) is 4.5.
Now, we have the complete five-number summary for the data set:
Minimum: 1
First Quartile (Q1): 1.5
Median (Q2): 3
Third Quartile (Q3): 4.5
Maximum: 7