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Use the table to answer the question.

This table presents the number of houses corresponding to different property values, showing the distribution of home prices in a given dataset.
Value per House Number of Houses
$150,000
2
$220,000
4
$490,000
3
$540,000
2
$800,000
5
$975,000
2
The values of several houses on Mango Street are displayed on the table. What is the median value of these houses?


(1 point)
$
Theo, Ara, Jose, and Dana all got 100 percent on their latest math test. Their scores on the previous six tests are listed. Whose mean test score will increase the most? (1 point)
Responses

Dana: 68, 74, 83, 80, 81, 82
Dana: 68, 74, 83, 80, 81, 82

Theo: 84, 88, 81, 85, 77, 76
Theo: 84, 88, 81, 85, 77, 76

Jose: 91, 93, 97, 96, 96, 96
Jose: 91, 93, 97, 96, 96, 96

Ara: 100, 98, 99, 97, 100, 100
The stem-and-leaf plot shows the speeds of the fastest steel roller coasters in Europe. The table shows the speeds of the fastest steel roller coasters in North America.

Speeds of the Fastest Steel Roller Coasters in Europe (in miles per hour)

This stem-and-leaf plot represents the speeds of the fastest steel roller coasters in Europe, where the stem indicates the tens digit and the leaf represents the ones digit.
Stem Leaf
7 4 5 5 5
8 0 0 3 4 8
9 9
11 1
Key: 7|4=74
miles per hour

Speeds of the Fastest Steel Roller Coasters in North America (in miles per hour)

This table displays the speeds of the fastest steel roller coasters in North America, categorized by country. The values represent speeds in miles per hour.
Canada 90 128 91
U.S. 93 120 100
Mexico 95 92 85
Find the range of the speeds of the fastest steel roller coasters on both continents.

(1 point)
The range of the speeds of the fastest steel roller coasters in Europe is
mph. The range of the speeds of the fastest steel roller coasters in North America is
mph.
Anthony wants to know the average daily high temperatures in his town during the summer. He chose two random samples of 10 consecutive days and recorded the daily high temperatures. The daily high temperatures in Fahrenheit are as follows.

Sample 1: 78 82 85 87 90 85 79 86 91 88
Sample 2: 81 79 80 86 89 92 82 88 84 87

Find the mean daily high temperatures of each sample and calculate the difference between these mean daily high temperatures. Express your answer as a decimal rounded to the nearest tenth.

(2 points)
The mean daily high temperature of Sample 1 is
°
.
The mean daily high temperature of Sample 2 is
°
.
The mean daily high temperatures of the two samples differ by
°
.
The data from two random samples of 100 students regarding what pet they own is given below.

This table presents data from two random samples of 100 students each, showing the number of students who own a dog, cat, or bird.
Dog Cat Bird Total
Sample 1 54 38 8 100
Sample 2 39 49 12 100
Based on the two samples, what percentage of students own a bird as a pet?

(1 point)
%

1 answer

Let's solve each question in order, starting with the median house value:

1. Median Value of the Houses

The values and their counts are as follows:

  • $150,000: 2 Houses
  • $220,000: 4 Houses
  • $490,000: 3 Houses
  • $540,000: 2 Houses
  • $800,000: 5 Houses
  • $975,000: 2 Houses

To find the median, we need to list out all values in order:

  • $150,000, $150,000 (2)
  • $220,000, $220,000, $220,000, $220,000 (4)
  • $490,000, $490,000, $490,000 (3)
  • $540,000, $540,000 (2)
  • $800,000, $800,000, $800,000, $800,000, $800,000 (5)
  • $975,000, $975,000 (2)

Putting them in order:

  • $150,000, $150,000, $220,000, $220,000, $220,000, $220,000, $490,000, $490,000, $490,000, $540,000, $540,000, $800,000, $800,000, $800,000, $800,000, $800,000, $975,000, $975,000

Total number of houses: 2 + 4 + 3 + 2 + 5 + 2 = 18 houses.

The median is the average of the 9th and 10th numbers in this ordered list:

  • 9th number: $490,000
  • 10th number: $540,000

Median = ($490,000 + $540,000) / 2 = $515,000

2. Mean Test Scores Increase

We will calculate the mean score for each student and the increase upon receiving a perfect score (100).

  • Dana:

    • Mean = (68 + 74 + 83 + 80 + 81 + 82) / 6 = 74.67 (approx.)
    • New mean = (74.67 * 6 + 100) / 7 = 81.14 (approx.)
    • Increase = 81.14 - 74.67 = 6.47

  • Theo:

    • Mean = (84 + 88 + 81 + 85 + 77 + 76) / 6 = 82.83 (approx.)
    • New mean = (82.83 * 6 + 100) / 7 = 86.04 (approx.)
    • Increase = 86.04 - 82.83 = 3.21

  • Jose:

    • Mean = (91 + 93 + 97 + 96 + 96 + 96) / 6 = 94.83 (approx.)
    • New mean = (94.83 * 6 + 100) / 7 = 96.69 (approx.)
    • Increase = 96.69 - 94.83 = 1.86

  • Ara:

    • Mean = (100 + 98 + 99 + 97 + 100 + 100) / 6 = 99.67 (approx.)
    • New mean = (99.67 * 6 + 100) / 7 = 99.86 (approx.)
    • Increase = 99.86 - 99.67 = 0.19

The student with the most significant increase is Dana, with an increase of approximately 6.47.

3. Range of Roller Coaster Speeds

Europe (from the stem-and-leaf plot):

  • Minimum speed = 74 mph
  • Maximum speed = 111 mph

Range = Max - Min = 111 - 74 = 37 mph

North America (from the table):

Speeds: 85, 90, 92, 93, 95, 100, 120, 128

  • Minimum speed = 85 mph
  • Maximum speed = 128 mph

Range = Max - Min = 128 - 85 = 43 mph

Summary of Ranges:

  • Europe: 37 mph
  • North America: 43 mph

4. Mean Daily High Temperatures

Sample 1:

Mean = (78 + 82 + 85 + 87 + 90 + 85 + 79 + 86 + 91 + 88) / 10 = 84.6°

Sample 2:

Mean = (81 + 79 + 80 + 86 + 89 + 92 + 82 + 88 + 84 + 87) / 10 = 84.8°

Difference:

Difference = 84.8 - 84.6 = 0.2°

5. Percentage of Bird Owners

In Sample 1:

  • Total bird owners = 8
  • Percentage = (8/100) * 100 = 8%

In Sample 2:

  • Total bird owners = 12
  • Percentage = (12/100) * 100 = 12%

Combined % across both samples:

  • Combined Total = 8 + 12 = 20
  • Total students = 100 + 100 = 200

Total percentage of students owning a bird = (20/200) * 100 = 10%.

Final Answers:

  1. Median House Value: $515,000
  2. Mean Increase: Dana's mean increases the most.
  3. Range for Europe: 37 mph, Range for North America: 43 mph.
  4. Mean temperatures differences: 0.2°.
  5. Percentage owning a bird: 10%.