Question

example 5. bob had an average score of 86 for the four tests he took during his first semester of math. during his second semester of math he took eight tests and had an average score of 92. what was his average for the entire year?
a. 87
b. 88
c. 89
d. 90
e. 91
solution. $\bar{x}=\frac{4(86)+8(92)}{4 + 8}=\frac{1080}{12}=90$
caution! do not simply average 86 and 92.
answer. d. 90

exercise 12. averages
solve.

1. the high temperature over a five - day period was 64.4°, 59.3°, 68.0°, 48.8°, and 53.6°. to the nearest tenth of a degree, what was the average high temperature for those days?
2. the memphis tigers basketball team averaged 78 points per game for the first six games of the season. what was the total number of points for those six games?
3. in first semester french class, joey had the following grades: three 80’s, two 90’s, and one 70. what was his semester average?
4. margie found she had an average english grade of 88 by dividing the sum of her five test scores by 5. she later found that she forgot to average in a test score of 82. what was her true average?
5. the total attendance at batesville junior high school for the 21 school days in march was 19,467. what was the average daily attendance?
6. total enrollment for each grade at hillview high school is 185 freshmen, 152 sophomores, 164 juniors, and 123 seniors. each grade is divided into sections: 5 freshman sections, 4 sophomore sections, 4 junior sections, and 3 senior sections. what is the average enrollment per section?

Explanation:

1.

Step1: Find the sum of temperatures

$64.4 + 59.3+68.0 + 48.8+53.6=294.1$

Step2: Calculate the average

$\text{Average}=\frac{294.1}{5}=58.82\approx58.8$

Use the formula $\text{Total}=\text{Average}\times\text{Number of games}$.
$\text{Total}=78\times6 = 468$

Step1: Calculate the sum of grades

$3\times80+2\times90 + 70=240+180 + 70=490$

Step2: Calculate the total number of grades

$3 + 2+1=6$

Step3: Calculate the average

$\text{Average}=\frac{490}{6}\approx81.7$

Answer:

$58.8^{\circ}$

2.