5.5 Averages and Probability

Before you get started, take this readiness quiz.

Simplify: $\frac{4 + 9 + 2}{3} .$
If you missed this problem, review the reference.

Simplify: $4 \left(8\right) + 6 \left(3\right) .$
If you missed this problem, review the reference.

Convert $\frac{5}{2}$ to a decimal.
If you missed this problem, review the reference.

Find the mean of the numbers $8 , 12 , 15 , 9 , \text{and} 6 .$

Find the mean of the numbers: $8 , 9 , 7 , 12 , 10 , 5 .$

Find the mean of the numbers: $9 , 13 , 11 , 7 , 5 .$

The ages of the members of a family who got together for a birthday celebration were $16 , 26 , 53 , 56 , 65 , 70 , 93 , \text{and} 97$ years. Find the mean age.

The ages of the four students in Ben’s carpool are $25 , 18 , 21 , \text{and} 22 .$ Find the mean age of the students.

Yen counted the number of emails she received last week. The numbers were $4 , 9 , 15 , 12 , 10 , 12 , \text{and} 8 .$ Find the mean number of emails.

For the past four months, Daisy’s cell phone bills were $\$\text{42}.\text{75} , \$\text{50}.\text{12} , \$\text{41}.\text{54} , \$\text{48}.\text{15} .$ Find the mean cost of Daisy’s cell phone bills.

Last week Ray recorded how much he spent for lunch each workday. He spent $\$\text{6}.\text{50} , \$\text{7}.\text{25} , \$\text{4}.\text{90} , \$\text{5}.\text{30} , \text{and} \$\text{12}.\text{00} .$ Find the mean of how much he spent each day.

Lisa has kept the receipts from the past four trips to the gas station. The receipts show the following amounts: $\$\text{34}.\text{87} , \$\text{42}.\text{31} , \$\text{38}.\text{04} , \text{and} \$\text{43}.\text{26} .$ Find the mean.

Find the median of the data set: $43 , 38 , 51 , 40 , 46 .$

Find the median of the data set: $15 , 35 , 20 , 45 , 50 , 25 , 30 .$

Find the median of the data set: $8 , 7 , 5 , 10 , 9 , 12 .$

Find the median of the data set: $21 , 25 , 19 , 17 , 22 , 18 , 20 , 24 .$

The number of sick days employees used last year: $3 , 6 , 2 , 3 , 7 , 5 , 6 , 2 , 4 , 2 .$ Identify the mode.

The number of handbags owned by women in a book club: $5 , 6 , 3 , 1 , 5 , 8 , 1 , 5 , 8 , 5 .$ Identify the mode.

The ages of the students in a statistics class are listed here: $19$, $20$, $23$, $23$, $38$, $21$, $19$, $21$, $19$, $21$, $20$, $43$, $20$, $23$, $17$, $21$, $21$, $20$, $29$, $18$, $28$. What is the mode?

Students listed the number of members in their household as follows: $6$, $2$, $5$, $6$, $3$, $7$, $5$, $6$, $5$, $3$, $4$, $4$, $5$, $7$, $6$, $4$, $5$, $2$, $1$, $5$. What is the mode?

The ski club is holding a raffle to raise money. They sold $100$ tickets. All of the tickets are placed in a jar. One ticket will be pulled out of the jar at random, and the winner will receive a prize. Cherie bought one raffle ticket.

ⓐ Find the probability she will win the prize.

ⓑ Convert the fraction to a decimal.

Ignaly is attending a fashion show where the guests are seated at tables of ten. One guest from each table will be selected at random to receive a door prize. ⓐ Find the probability Ignaly will win the door prize for her table. ⓑ Convert the fraction to a decimal.

Hoang is among $20$ people available to sit on a jury. One person will be chosen at random from the $20 .$ ⓐ Find the probability Hoang will be chosen. ⓑ Convert the fraction to a decimal.

Three women and five men interviewed for a job. One of the candidates will be offered the job.

ⓐ Find the probability the job is offered to a woman.

ⓑ Convert the fraction to a decimal.

A bowl of Halloween candy contains $5$ chocolate candies and $3$ lemon candies. Tanya will choose one piece of candy at random. ⓐ Find the probability Tanya will choose a chocolate candy. ⓑ Convert the fraction to a decimal.

Dan has $2$ pairs of black socks and $6$ pairs of blue socks. He will choose one pair at random to wear tomorrow. ⓐ Find the probability Dan will choose a pair of black socks ⓑ Convert the fraction to a decimal.

Find the mean.

$3$, $8$, $2$, $2$, $5$

Find the mean.

$65$, $13$, $48$, $32$, $19$, $33$

Find the mean.

$202$, $241$, $265$, $274$

Find the mean.

$12.45$, $12.99$, $10.50$, $11.25$, $9.99$, $12.72$

Find the mean.

Four girls leaving a mall were asked how much money they had just spent. The amounts were $\$\text{0}$, $\$\text{14}.\text{95}$, $\$\text{35}.\text{25}$, and $\$\text{25}.\text{16}$. Find the mean amount of money spent.

Find the mean.

The number of minutes it took Jim to ride his bike to school for each of the past six days was $21$, $18$, $16$, $19$, $24$, and $19$. Find the mean number of minutes.

Find the mean.

The top eight hitters in a softball league have batting averages of $.373$, $.360$, $.321$, $.321$, $.320$, $.312$, $.311$, and $.311$. Find the mean of the batting averages. Round your answer to the nearest thousandth.

Find the median.

$24$, $19$, $18$, $29$, $21$

Find the median.

$65$, $56$, $35$, $34$, $44$, $39$, $55$, $52$, $45$

Find the median.

$4$, $8$, $1$, $5$, $14$, $3$, $1$, $12$

Find the median.

$99.2$, $101.9$, $98.6$, $99.5$, $100.8$, $99.8$

Find the median.

Last week Ray recorded how much he spent for lunch each workday. He spent $\$\text{6}.\text{50}$, $\$\text{7}.\text{25}$, $\$\text{4}.\text{90}$, $\$\text{5}.\text{30}$, and $\$\text{12}.\text{00}$. Find the median.

Find the median.

Brian is teaching a swim class for $6$ three-year olds. Their ages, in months, are $38 , 41 , 45 , 36 , 40 , \text{and} 42 .$ Find the median age.

Identify the mode.

$2$, $5$, $1$, $5$, $2$, $1$, $2$, $3$, $2$, $3$, $1$

Identify the mode.

$18$, $22$, $17$, $20$, $19$, $20$, $22$, $19$, $29$, $18$, $23$, $25$, $22$, $24$, $23$, $22$, $18$, $20$, $22$, $20$

Identify the mode.

The number of children per house on one block: $1$, $4$, $2$, $3$, $3$, $2$, $6$, $2$, $4$, $2$, $0$, $3$, $0 .$

Identify the mode.

The number of units being taken by students in one class: $12$, $5$, $11$, $10$, $10$, $11$, $5$, $11$, $11$, $11$, $10$, $12$.

Express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

Josue is in a book club with $20$ members. One member is chosen at random each month to select the next month’s book. Find the probability that Josue will be chosen next month.

Express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

There are $24$ people who work in Dane’s department. Next week, one person will be selected at random to bring in doughnuts. Find the probability that Dane will be selected. Round your answer to the nearest thousandth.

Express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

Michel has four rock CDs and six country CDs in his car. He will pick one CD to play on his way to work. Find the probability Michel will pick a rock CD.

Express the probability as both a fraction and a decimal. (Round to three decimal places, if necessary.)

Donovan is considering transferring to a $\text{4}-\text{year college} .$ He is considering $10$ out-of state colleges and $4$ colleges in his state. He will choose one college at random to visit during spring break. Find the probability that Donovan will choose an out-of-state college.

Joaquin gets paid every Friday. His paychecks for the past $8$ Fridays were $\$\text{315} ,$ $\$\text{236}.\text{25} ,$ $\$\text{236}.\text{25} ,$ $\$\text{236}.\text{25} , \$\text{315} ,$ $\$\text{315} ,$ $\$\text{236}.\text{25} ,$ $\$\text{393}.\text{75} .$ Find the ⓐ mean, ⓑ median, and ⓒ mode.

Explain in your own words the difference between the mean, median, and mode of a set of numbers.