Math Problem Statement

An intelligence test was administered to 8 people, and their respective completion times (in minutes) were: 43, 26, 44, 28, 35, 31, 43, 32. What are the median, mean, and mode of this dataset?

Solution

The image displays an intelligence test completion dataset and asks to compute the following:

  1. Median: The middle value of the ordered dataset.
  2. Mean: The average of all the values.
  3. Mode: The most frequent value(s) in the dataset.

Given the dataThe image displays an intelligence test completion dataset and asks to compute the following:

  1. Median: The middle value of the ordered dataset.
  2. Mean: The average of all the values.
  3. Mode: The most frequent value(s) in the dataset.

Given the

  • Completion times (in minutes): 43, 26, 44, 28, 35, 31, 43, 32

Let's start by calculating these statistics.Here are the results based on the given dataset:

  1. Median: 33.5 minutes
  2. Mean: 35.3 minutes (rounded to one decimal place)
  3. Mode: 43 minutes, which appears twice.

Would you like further clarification or more details on any of these calculations?

Here are five related questions for further exploration:

  1. How would adding another data point affect the median?
  2. What is the difference between mean, median, and mode in skewed datasets?
  3. How do you calculate the weighted mean if different completion times had different weights?
  4. What happens to the mean and median if an outlier (e.g., 60 minutes) is introduced into the dataset?
  5. How can you calculate the range and standard deviation for this dataset?

Tip: The median is less sensitive to outliers compared to the mean, making it a more robust measure of central tendency in skewed data.

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Math Problem Analysis

Mathematical Concepts

Measures of Central Tendency
Descriptive Statistics

Formulas

Median = Middle value of an ordered data set
Mean = Sum of all values / Number of values
Mode = Most frequently occurring value

Theorems

None

Suitable Grade Level

Grades 6-8