Intro to Stat 3.1
When an observation that is much larger than the rest of the data is added to a data set, the value of the mean will __________________.
increase.
For a distribution that is symmetric, which of the following is true?
mean = median
The _______ is a parameter that is computed using data from all the individuals in a population.
population arithmetic mean, μ (pronounced "mew") ; To compute the population mean, μ, add all the data values (test scores) and then divide by the number of individuals in the population.
A numerical summary of data is said to be______ if observations that are extreme (very large or small) relative to the data do not affect its value substantially. (So the median is resistant, but the mean is not resistant.)
resistant
The ______ is a statistic that is computed using data from individuals in a sample.
sample arithmetic mean, x (pronounced "x-bar"),
Finding the mean (Odd Number)
1. Arrange the data in ascending order 2. Find n = observations (The median is the data value exactly in the middle)
Finding the mean (Even Number)
1. Arrange the data in ascending order 2. Find n = observations (The median is the mean of the two middle) 3. M = Middle1 + Middle2 / 2
The _____ of a variable is the value that lies in the middle of the data when arranged in ascending order. We use M to represent the median.
Median Stat > Summary Stats > Columns > Median > Compute If the number of observations is even, then the median is the mean of the two middle observations in the data set. That is, the median is the mean of the observations that lie in the n/2 position and the n/2 +1 position.
For a distribution that is skewed left, which of the following is true?
Median > Mean
Describing the Shape of a Distribution
1. Find the mean and median 2. Describe the shape (Graph > Histogram > Compute) 3. Which measure of central tendency better describe ____? (Mean - Symmetric or similar) (Median - Skewed)
The _________ of a variable is computed by adding all the values of the variable in the data set and dividing by the number of observations.
Arithmetic Mean
When a data set has two modes we would say that the data are _____. If a data set has three or more modes, then we say that the data are _______
Bimodal; Multimodal
A data set will always have exactly one mode. T/F
False
When an observation that is much larger than the rest of the data is added to a data set, the value of the median will increase substantially. T/F
False
The U.S. Department of Housing and Urban Development (HUD) uses the median to report the average price of a home in the United States. Why do you think HUD uses the median?
HUD uses the median because the data are skewed right.
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 sample size, state what happens to the mean and median. For each sample size, the mean __________ , and the median __________ Comment on the role that the number of observations plays in resistance.
Increases, remains mostly constant ; As the sample size increases, the impact of the misrecorded data on the mean decreases.
For a distribution that is skewed right, which of the following is true?
Mean > Median
The ____ of a variable is the observation of the variable that occurs most frequently in the data set.
Mode
Steps to compute a population mean and a sample mean
Part A) Compute the population mean μ (Stat > Summary Stats > Columns > Numerical data column > Mean > Compute) Part B) Find a simple random sample of the n = ___ students (Data > Sample > Both columns > Input sample size > Sample all columns at once > Compute) Part C) Compute the sample mean (x bar) (Stat > Summary Stats > Columns > Sample > Mean )
Why is the median resistant, but the mean is not?
The mean is not resistant because when data are skewed, there are extreme values in the tail, which tend to pull the mean in the direction of the tail. The median is resistant because the median of a variable is the value that lies in the middle of the data when arranged in ascending order and does not depend on the extreme values of the data.
The median for the given set of six ordered data values is 26.5. 9 12 21 _ 41 49 What is the missing value?
The missing value is 32.
Do you think it would be a good idea to rotate the candidate choices in the question? Why?
Yes, to avoid response bias
Find the population mean or sample mean as indicated. Sample: 17, 15, 5, 7, 11
x = 11