Here are the IQ test scores of 10 randomly chosen fifth-grade students: 143 136 124 121 126 133 97 109 117 118 The mean of these scores (rounded to one decimal place) is .
The Correct Answer and Explanation is:
To find the mean IQ score of the 10 randomly chosen fifth-grade students, follow these steps:
Step 1: Add all the IQ scores
The scores are:
143, 136, 124, 121, 126, 133, 97, 109, 117, 118
Now add them together:
143 + 136 + 124 + 121 + 126 + 133 + 97 + 109 + 117 + 118 = 1224
Step 2: Divide the total by the number of students
There are 10 students.
So the mean =
1224 รท 10 = 122.4
Final Answer:
The mean IQ score is 122.4
Explanation
The mean, often referred to as the average, is a measure of central tendency used in statistics to represent a typical value in a data set. In this question, we are given the IQ scores of ten fifth-grade students and asked to find the mean score.
To begin, we add all the IQ values together. This total sum represents the combined intellectual scores of the group. Summing individual values like 143, 136, and so on gives us a total of 1224.
Next, to compute the mean, we divide this total by the number of values in the set, which in this case is 10. This division is necessary because the mean is defined as the total of all values divided evenly among the number of data points. Doing this yields 122.4.
The mean tells us that, on average, these students have an IQ of 122.4. This is slightly above the population average IQ, which is typically around 100. This may suggest that this group of students, on average, performs above the expected norm. However, it’s important to note that with a small sample size like this, outliers (such as the score of 97) can have a noticeable impact on the mean.
Using the mean gives us a simple way to describe the overall performance of the group and can be helpful in comparing different groups or identifying trends in academic settings.
