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 {8,8,9,9,9,10,10}. choose the correct answer below. low value = \square lower quartile = \square median = \square upper quartile = \square high value = \square

Explanation:

Step1: Order the data

The set is {8,8,9,9,9,10,10}. It is already in ascending order.

Step2: Find low value

The lowest value (minimum) is the first element, so low value = 8.

Step3: Find median (middle value)

For \( n = 7 \) (odd), the median is the \( \frac{n + 1}{2}=4^{\text{th}} \) term. The 4th term is 9, so median = 9.

Step4: Find lower quartile (Q1)

The lower half is {8,8,9} (first 3 terms, since median is the 4th term, we take first \( \frac{n - 1}{2}=3 \) terms for lower half). The median of the lower half (Q1) is the 2nd term (since \( n_{\text{lower}} = 3 \), median is \( \frac{3 + 1}{2}=2^{\text{nd}} \) term), which is 8. So lower quartile = 8.

Step5: Find upper quartile (Q3)

The upper half is {9,10,10} (last 3 terms). The median of the upper half (Q3) is the 2nd term (since \( n_{\text{upper}} = 3 \), median is \( \frac{3 + 1}{2}=2^{\text{nd}} \) term), which is 10. So upper quartile = 10.

Step6: Find high value

The highest value (maximum) is the last element, so high value = 10.

Answer:

low value = 8
lower quartile = 8
median = 9
upper quartile = 10
high value = 10