Math Problem Statement

The following sample IQ scores were obtained from a group of four-year-old children: 120, 65, 78, 80, 104. Find the median and mean.

Solution

The problem asks to find the median and mean of the given IQ scores:

120, 65, 78, 80, 104120, \ 65, \ 78, \ 80, \ 104

1. Mean (Average):

The mean is calculated by summing up all the values and dividing by the total number of values.

Mean=120+65+78+80+1045=4475=89.4\text{Mean} = \frac{120 + 65 + 78 + 80 + 104}{5} = \frac{447}{5} = 89.4

2. Median:

To find the median, first arrange the scores in ascending order: 65, 78, 80, 104, 12065, \ 78, \ 80, \ 104, \ 120

Since there are 5 numbers (an odd number), the median is the middle value, which is 80.

Final Answer:

  • Mean: 89.4
  • Median: 80

Would you like more details or have any further questions?

Here are 5 related questions for further practice:

  1. What is the mode of the given data set?
  2. If a new IQ score of 90 is added, what would be the new mean?
  3. What is the range of the given IQ scores?
  4. If the lowest score is removed, how does the median change?
  5. Can the mean be affected more by extreme values than the median? Why?

Tip: The median is a better measure of central tendency than the mean when dealing with outliers.

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Math Problem Analysis

Mathematical Concepts

Statistics
Measures of Central Tendency

Formulas

Mean = (Sum of values) / (Number of values)
Median = Middle value in a sorted list (if odd number of values)

Theorems

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Suitable Grade Level

Grades 6-8