Resistance and Sample Size Each of the following three data...

Resistance and Sample Size Each of the following three data sets represents the IQ scores of a random sample of adults. IQ scores are known to have a mean and median of 100. For each data set, determine the mean and median. For each data set recalculate the mean and median, assuming that the individual whose IQ is 106 is accidentally recorded as $160 .$ For each sample size, state what happens to the mean and the median. Comment on the role the number of observations plays in resistance. (FIGURE CAN'T COPY)

Key Concepts

Sample Size

Sample size plays a crucial role in statistical analysis because larger samples tend to provide more reliable estimates of the population parameters. With a larger sample, the impact of an individual outlier is diminished when calculating the mean, while the median continues to be resistant. Conversely, in smaller samples, an outlier can have a more pronounced effect on the mean, highlighting the importance of sample size in determining the robustness of summary statistics.

Resistance

Resistance refers to the ability of a statistical measure to remain relatively unchanged when outliers or extreme values are present in the data. In this context, the median is considered resistant because it does not change much with an individual extreme value, whereas the mean is less resistant and can be significantly altered by such values.

Mean

The mean is the arithmetic average of a data set and is calculated by summing all the observations and dividing by the number of observations. It is sensitive to outliers because extreme values can skew the sum, thereby affecting the overall average, even when the majority of the data remains unchanged.

Median

The median is the middle value of an ordered data set and represents the central tendency in a way that is not as influenced by extreme values or outliers as the mean. It is a more robust measure of location when the data contains anomalies or errors.

Transcript

00:01 Okay, so for number 33 in section 3 .1, we're talking about how resistance and sample size can differ.

00:10 So we're given a sample size of five iq scores, 12 iq scores, and then a sample size of 30 iq scores.

00:18 The first thing we are asked to do is to find the mean and median for each.

00:25 So we're going to go ahead and identify that.

00:28 So with the one that had a sample size of five, there was a mean where you add up all five numbers, the 106, 92, 98, 103, and 100, you add up all those numbers.

00:49 You get 499, and you're going to divide that by five.

00:55 So 499 to out by five is going to be 99.

01:00 Then the median is going to be the middle number when they're ordered from smallest to largest.

01:09 So that middle number should be 100.

01:14 Okay.

01:15 Then we move on to find when the sample size was 12, you'd go get that mean and median.

01:29 So you add up the 106, 92, 98, 103, 100, 102, 92, 83, 708, and 1201, all 12 numbers.

01:43 When you add up all 12 numbers, you should get 1205, oh, and then divide that by 12.

01:51 You should get a iq average of 100 .4.

01:59 Okay.

02:01 Then the median would be whatever number is between the sixth and the seventh term when you reorder all those numbers from smallest to largest.

02:10 So those two numbers should be 100 and 102.

02:14 So you take the 100 and the 102, cut it in half.

02:19 It's going to be a median of 101 with the sample size of 12.

02:24 Then when our sample size is 30, you're going to add up all 30 numbers to get the mean.

02:34 So we add up everything in each column from the 106 all the way over to the 103 in that lower right corner of your table.

02:43 You add up all 30 numbers.

02:45 You should get a total of 3 ,017, divide that by 30, and that's going to be 100.

02:55 Six approximately.

02:57 You're going to do the same thing...

Please give Ace some feedback