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} b. give the five - number summary and draw a boxplot for each set. give the five - number summary for set {9,9,9,9,9,9,9}. low value = lower quartile = median = upper quartile = high value =

Explanation:

Step1: Identify the low value

The set is {9,9,9,9,9,9,9}. The smallest number (low value) in this set is 9.

Step2: Identify the lower quartile

For a set with 7 data points (odd number), the position of the lower quartile (Q1) is at the \(\frac{n + 1}{4}\)th term. \(n = 7\), so \(\frac{7+1}{4}=2\)nd term. All terms are 9, so Q1 = 9.

Step3: Identify the median

The median (middle term) for 7 data points is at the \(\frac{n + 1}{2}\)th term. \(\frac{7 + 1}{2}=4\)th term. The 4th term is 9, so median = 9.

Step4: Identify the upper quartile

The position of the upper quartile (Q3) is at the \(\frac{3(n + 1)}{4}\)th term. \(\frac{3(7 + 1)}{4}=6\)th term. All terms are 9, so Q3 = 9.

Step5: Identify the high value

The largest number (high value) in the set is 9.

Answer:

low value = \(\boldsymbol{9}\)
lower quartile = \(\boldsymbol{9}\)
median = \(\boldsymbol{9}\)
upper quartile = \(\boldsymbol{9}\)
high value = \(\boldsymbol{9}\)