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