Question

the following four sets of 7 numbers all have a mean of 9. complete parts (a) through (d) below. {9,9,9,9,9,9,9} , {8,8,9,9,9,10,10} , {6,6,6,9,12,12,12} , {4,4,4,9,14,14,14} give the five - number summary for set {4,4,4,9,14,14,14}. low value = \square lower quartile = \square median = \square upper quartile = \square high value = \square

Explanation:

Step1: Identify Low and High Values

The set is {4,4,4,9,14,14,14}. The smallest number (low value) is 4, and the largest (high value) is 14.

Step2: Find the Median

For a set with 7 (odd) numbers, the median is the 4th term. The ordered set is [4,4,4,9,14,14,14], so the 4th term is 9.

Step3: Calculate Lower Quartile (Q1)

The lower half of the set (excluding median) is {4,4,4}. The median of this subset (Q1) is the 2nd term (or average, but all are 4), so Q1 = 4.

Step4: Calculate Upper Quartile (Q3)

The upper half of the set (excluding median) is {14,14,14}. The median of this subset (Q3) is the 2nd term (or average, all 14), so Q3 = 14.

Answer:

low value = 4
lower quartile = 4
median = 9
upper quartile = 14
high value = 14