Math Problem Statement

Professor Avila administered his final exam to his class of 12 students. The following raw scores represent points on his 100-item multiple choice exam where one point was awarded for each correct answer, and scores could range from 0-100.

Anderson .Paak 77 TROPA MAGICA 91 Chromatics 82 A Tribe Called Quest 68 Janet Jackson 95 Talking Heads 88 Selena 90 Chet Faker 77 Kendrick Lamar 85 Whitney Houston 55 Doechii 59 Bad Bunny 69

  1. Calculate the mean (round to the hundredths place):

  2. Find the median:

  3. Find the mode:

Solution

1. Calculate the Mean:

To find the mean, sum all the raw scores and divide by the total number of students.

Given the scores:

  • Anderson .Paak: 77
  • TROPA MAGICA: 91
  • Chromatics: 82
  • A Tribe Called Quest: 68
  • Janet Jackson: 95
  • Talking Heads: 88
  • Selena: 90
  • Chet Faker: 77
  • Kendrick Lamar: 85
  • Whitney Houston: 55
  • Doechii: 59
  • Bad Bunny: 69

Step 1: Add all the scores: 77+91+82+68+95+88+90+77+85+55+59+69=88477 + 91 + 82 + 68 + 95 + 88 + 90 + 77 + 85 + 55 + 59 + 69 = 884

Step 2: Divide the total sum by the number of students (12): Mean=88412=73.67\text{Mean} = \frac{884}{12} = 73.67

So, the mean score is 73.67.

2. Find the Median:

To find the median, first, arrange the scores in ascending order:

  • 55, 59, 68, 69, 77, 77, 82, 85, 88, 90, 91, 95

The median is the middle value. Since there are 12 numbers (an even amount), the median is the average of the two middle values (6th and 7th in the sorted list).

Step 1: Identify the middle values:

  • The 6th score is 77.
  • The 7th score is 82.

Step 2: Find the average of these two values: Median=77+822=1592=79.5\text{Median} = \frac{77 + 82}{2} = \frac{159}{2} = 79.5

So, the median score is 79.5.

3. Find the Mode:

The mode is the score that occurs most frequently. From the list of scores:

  • 77 appears twice.
  • No other score appears more than once.

Thus, the mode is 77.


Summary:

  1. Mean = 73.67
  2. Median = 79.5
  3. Mode = 77

Would you like more details on how these values were calculated? Feel free to ask for clarifications.

Here are 5 related questions you might be interested in:

  1. How do you calculate the range of these scores?
  2. What is the standard deviation of these scores?
  3. How do you interpret the mode, median, and mean in the context of a class exam?
  4. How does changing one student's score affect the mean and median?
  5. What would happen to the mean if a score of 100 was added?

Tip: The median is less sensitive to extreme values compared to the mean, which is helpful in understanding data when there are outliers!

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency

Formulas

Mean = Sum of all values / Number of values
Median = Middle value in ordered data (average of two middle values if even count)
Mode = Most frequent value

Theorems

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Suitable Grade Level

Grades 6-8