Money, money, money (simple interest)
What is the principal amount?
The beginning amount (loan/savings)
Before editing, a movie is 120 minutes long. The edited movie is 25% shorter. What is the length of the edited movie?
90-minutes
What is the difference between a random sample and a representative sample?
Random: equal chance of sample
Representative: specific audience with bias
Qualitative: broad
Quantitative: numerical, counting, select options
Draw the difference between a dot plot and a box plot.
Check drawing
The sales tax at a hotel is 18%. A standard room costs $98 before tax. What is the total cost of a standard room?
$115.64
A payment increases from $700 to $945. What is the percent increase in the payment?
35%
Vivian surveys a random sample of Grade 7 students in the school band. She asks the students how many text messages they send each day. The median of her sample data is 50.
Edward surveys a random sample of all Grade 7 students at the school. He asks the students how many text messages they send each day. The median of his sample data is 60.
Whose result is more likely to be representative of all the Grade 7 students at the school?
Edward: all Grade 7
What type of data would I be collecting if I was asking 30 students if they would prefer or not prefer uniforms?
Quantitative
Define and show the formulas for median absolute deviation and interquartile range.
Mean absolute deviation: average distance of each data value from the mean.
Interquartile range: the difference between the ends of the box. The range of the middle 50% of the data.
Suppose you deposit $1,200 into a bank account. The account earns yearly simple interest at a rate of 1.75%. How many years does it take to earn a total of $126 in simple interest?
6-years
One year, an estimated 598,000 cranes migrated in March. The next March, an estimated 660,000 cranes migrated. To the nearest integer percent, what is the percent change in the number of migrating cranes? Is this a percent increase or a percent decrease?
10% increase
An assistant at an animal shelter wants to know the typical age of dogs admitted to the shelter. The shelter has admitted 353 dogs. Each dog has an ID number. How could the assistant select a representative sample of the dogs and use it to gain information about the population?
Various examples
Qualitative
The students in a science class take a quiz before they start a new unit. The mean score is 3 and the MAD is 1.8. After the unit, the students take the quiz again. The mean score is 7.5 and the MAD is 1.5. Suppose you plotted the scores for both quizzes. Would you expect to see a lot of overlap? Explain.
Not really.
The owner of a store buys wooden benches for $50 each. She marks up the price by 75%. For the last week of the season, she sells the remaining benches for 30% off. How much profit does the owner make on each bench sold during the last week of the season?
$61.25
The original cost of a shirt is $40. A store manager marks up the cost by 20% to get the selling price. During a sale, the store manager marks down the cost of the shirt by 20%. What is the percent change from the original cost of the sale price? Is this a percent increase or a percent decrease?
4% decrease
Mr. Shen selects 20 of his 140 students at random to survey about their pets. His survey indicates that 8 students have a dog, 9 students have a cat, 3 students have another kind of pet, and 5 students have no pets. How many of his students should Mr. Shen expect to have a cat?
63 students
Kindergarten is celebrating national art day and was asked to share what their favorite color was out of 5 options. One of the 5 options is "other". What type of data is being collected?
Qualitative (only because of "other" option).
A box contains a mix of 800 golf balls. Some are white and the rest are purple. Each student in Mrs. Ramirez's class selects a random sample of 20 golf balls from the box, counts the purple golf balls, and returns the sample to the box.
1 student: 2 purple
1 student: 4 purple
3 students: 5 purple
5 students: 6 purple
1 student: 7 purple
1 student: 8 purple
220 purple balls
The total simple interest owed on a loan of $8,000 after 60 months is $1,280. What is the yearly interest rate on the loan?
3.2%
Elijah estimates that 54 students will be at the school dance. Alano estimates 45 students will be. There are actually 48 students at the dance. How much less is the percent error in Alano's estimate than in Elijah's estimate? Round to nearest one-hundredth percent.
4.75%
A school has 800 students. The principal plans to order a tote bags for each student. They ask 120 students selected at random which color bag they prefer. Here was their data:
48: Blue
54: Black
18: Gray
Based on the sample, how many bags of each color should the principal order?
320 Blue
360 Black
120 Gray
I am wanting to figure out the average time that 30 students spend on their homework each week. What type of data am I collecting?
Quantitative (because numerical data).
10. Make a box plot based on the following information about students studying for Math test:
Minimum: 30-minutes
Lower Quartile: 1-hour
Median: 1.5 hours
Upper Quartile: 2 hours
Maximum: 3 hours
See visual