Question

(effects of changes in data mc)
the list represents the ages of students in a gymnastics class.
5, 7, 6, 9, 7, 5, 8, 8, 6, 9
if another student of age 5 joins the class, how is the mean affected?
○ the mean will remain the same at 7.
○ the mean will remain the same at about 6.3.
○ the mean will increase to about 7.2.
○ the mean will decrease to about 6.8.

question 7 (multiple choice worth 2 points)
(areas of triangles, quadrilaterals, and composite figures mc)
what is the area of a right triangle with a base of 7 feet and a height of 14 feet?
○ 98 ft²
○ 49 ft²
○ 35 ft²
○ 28 ft²

Explanation:

Question 6

Step1: Calculate original sum and mean

Original data: \(5, 7, 6, 9, 7, 5, 8, 8, 6, 9\)
Sum: \(5 + 7 + 6 + 9 + 7 + 5 + 8 + 8 + 6 + 9 = 70\)
Number of data points: \(n = 10\)
Original mean: \(\frac{70}{10} = 7\)

Step2: Calculate new sum and mean

New data includes an additional \(5\).
New sum: \(70 + 5 = 75\)
New number of data points: \(n = 11\)
New mean: \(\frac{75}{11} \approx 6.8\)

Step1: Recall area formula for triangle

The area of a triangle is given by \(A = \frac{1}{2} \times \text{base} \times \text{height}\).

Step2: Substitute values

Base \(= 7\) ft, Height \(= 14\) ft.
\(A = \frac{1}{2} \times 7 \times 14 = \frac{98}{2} = 49\)

Answer:

The mean will decrease to about 6.8.

Question 7