Download CC Math 1 Unit 2 Test Review KEY 1. The table below shows the

CC Math 1
Unit 2 Test Review KEY
1. The table below shows the daily attendance at two movie theaters over a period of 5 days. Calculate the mean and
median for each and answer the questions below.
Day 1
Day 2
Day 3
Day 4
Day 5
Carmike Cinemas
100
87
90
10
91
IMAX Theater 2
72
97
70
71
100
Mean
Median
75.6
90
82
72
Which measure of center would you use to describe the typical daily attendance for the 5 days at Carmike Cinemas?
Explain your choice.
I would use the median. Day 4’s attendance of 10 lowered the mean significantly, so the median is a more accurate
representation of the typical daily attendance.
Which measure of center would you use to describe the typical daily attendance for the 5 days at IMAX Theater 2?
Explain your choice.
I would use the mean because the median gives us an artificially low number. It does not reflect the two days of high
attendance.
2. Our school has to select a female athlete to send to the regional championship for the long jump event. Three girls are
in contention. A jump-off was held to determine who will advance to the regional championship.
Their results, in meters, are given in the chart.
Arnold says, “Eliza has the longest average. She should go to the
regional championship.”
Do you think Arnold is right? Is Eliza the best choice? Explain
your reasoning.
Phoebe
3.25
3.95
4.28
2.95
3.66
3.81
Helga
3.55
3.88
3.61
3.97
3.75
3.59
Eliza
3.7
3.78
3.92
3.62
3.85
3.73
Phoebe’s average jump = 3.650 meters
Helga’s average jump = 3.725
Eliza’s average jump = 3.767
I think Arnold is right. Eliza is the best choice. Looking at the average jump for each female, it is obvious that Eliza can
jump the furthest distance.
3. Sarah shopped for clothing every Saturday for the past 6 weeks. She spent the following amounts:
$109, $72, $99, $15, $99, and $89.
a. Calculate the mean and median of Sarah’s purchases.
mean = $80.50
median = $94.00
b. Which measure of center would Sarah tell her parents to convince them that she is not spending too much money on
clothes? Explain your choice.
Sarah would use the mean. It is a smaller value than the median and would imply that she is not spending as much
money as if she told them the median value.
c. Which value would Sarah tell her parents to convince them that she needs an increase in her allowance? Explain.
Sarah would use the median. In order to purchase all of the clothing items for $94 (which is obviously more than
$80.50), she would need more money, or an increase in her allowance.
4. Which table contains data whose distribution would be skewed left?
Table C. When the shape is skewed left, we know that there are a lot of high values in our data.
A.
B.
C.
D.
5. You are planning to take a part-time job as a server at a local restaurant. During your interview, the restaurant
manager told you that their best server, Leo, made an average of $70 in tips each night last week. However, when you
asked Leo about this, he said that he made an average of only $50 each night last week. He provides you with a copy of
his nightly tip amounts from last week.
Day
Tip Amount
Sunday
$50
Monday
$45
Wednesday $48
Friday
$125
Saturday
$85
a. Calculate the mean and the median tip amount.
mean = $70.60
median = $50.00
b. Which value is Leo’s boss using to describe the average tip amount? Why do you think he chose this value?
Leo’s boss is using the mean. The mean amount is higher, so it would make someone think that he/she would
earn about $70 each night.
c. Which value is Leo using? Why do you think he chose this value?
Leo is using the median. It is a more realistic representation of what Leo actually earned each night.
d. Which value best describes the typical amount of tips per night? Explain your choice.
The median. Friday night’s tips ($125) were much higher and made the mean higher as a result. The median is
a more accurate representation of how much money was typically earned throughout the week.
6. Why does the shape of the distribution of test scores on a really easy test tend to be skewed to the left?
Most students do very well on a really easy test, which results in a lot of high scores, with only a few low scores at
times.
7. Why does the shape of the distribution of heights of the male students at your school tend to be symmetrical?
Most students tend to be about the same height, with a few short students (low outliers) and a few tall students (high
outliers).
8. On last week’s science test, Ms. Guthrie’s class had an average of 83 points with a standard deviation of 8 points. Mrs.
Powell’s class had an average of 78 points with a standard deviation of 4 points. Which class was more consistent with
their test scores? How do you know?
Ms. Powell’s class was more consistent with their test scores. I know this because the standard deviation is lower,
which means the test scores are closer to the average score of 78.
9. A police officer was studying traffic patterns in one part of town. In this study, he
recorded the speeds of 17 cars traveling in a 40 mph zone. Here are the speeds in miles
per hour:
35, 40, 42, 43, 45, 46, 37, 38, 52, 39, 47, 42, 41, 39, 54, 52, 25
25, 35, 37, 38, 39, 39, 40, 41, 42, 42, 43, 45, 46, 47, 52, 52, 54
For this set of data, construct a histogram using the intervals 21-25, 26-30, 31-35, 36-40, 41-45, 46-50, and
51-55.
Additionally, describe the shape, center, spread (range), and outliers of your histogram.
Shape: skewed left
Center:
Remember that we know how to describe data graphically (with histograms) and numerically
(mean/median). If you have a question similar to this one on the test, you can specifically state the
appropriate measure of center (mean or median).
1. If we only looked at the histogram, we would say 36-45 since there are two intervals of equal
length.
2. If we were to state the mean or median, we would state the median because of the outlier (25),
so the median is 42 mph.
Spread: 25 - 54
Range: 29
Outliers: 25
10. Create a box plot for the data. {2, 3, 5, 5, 6, 7, 7, 9, 9}
Min: 2
Q1 (lower quartile): 4
Median: 6
Q3 (upper quartile): 8
Max: 9
1
10