Module 1- Central Tendency

The square root of the variance is the_________________________

Standard Deviation

How do you calculate the Range?

Take maximum value and subtract minimum value

For any data set, which measures of central tendency have only one value?

The median and mean can only have one value for a given data set. The mode can have more than one value

What kind of data is a temperature reading?

nominal data ->interval data ordinal data ratio data

Measures of dispersion attempt to describe

the spread of the data values in a data set.

If you are comparing the number of girls to the number of boys in a classroom, you are gathering

-> ratio data. nominal data. ordinal data. interval data.

The variance for a population is calculated by:

1. Finding the mean(the average). 2. Subtracting the mean from each number in the data set and then squaring the result. The results are squared to make the negatives positive. Otherwise negative numbers would cancel out the positives in the next step. It's the distance from the mean that's important, not positive or negative numbers. 3. Averaging the squared differences.

What are the three main measure of tendency?

1. Mean 2. Median 3. Mode

Standard deviation is used for measuring______________

Dispersion

Outliers

are extreme, or atypical data value(s) that are notably different from the rest of the data

Mean

the average of the data

Median

the middle value of the ordered data

What is the most appropriate measure of central tendency when the data has outliers?

The median is usually preferred in these situations because the value of the mean can be distorted by the outliers. (However, it will depend on how influential the outliers are. If they do not significantly distort the mean, using the mean as the measure of central tendency will usually be preferred.)

Why is it is important to detect outliers within a distribution?

because they can alter the results of the data analysis.

What does Variance measure?

how far a data set is spread out. (The technical definition is "The average of the squared differences from the mean," but all it really does is to give you a very general idea of the spread of your data. A value of zero means that there is no variability; All the numbers in the data set are the same)

Sally is studying the grade ranking of the senior class. She is gathering which kind of data?

interval nominal ratio -> ordinal

When is the mode the best measure of central tendency?

The median is usually preferred to other measures of central tendency when your data set is skewed (i.e., forms a skewed distribution) or you are dealing with ordinal data.

In a normally distributed data set, which is greatest: mode, median or mean?

If the data set is perfectly normal, the mean, median and mean are equal to each other (i.e., the same value).

When is the mean the best measure of central tendency?

The mean is usually the best measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data is normally distributed.

Skewness is

a measure of degree of asymmetry of the distribution

What is Measure of central tendency?

is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or center of its distribution.

Dispersion

is a way of describing how spread out a set of data is (When a data set has a large value, the values in the set are widely scattered; when it is small the items in the set are tightly clustered).

What is an Interquartile Range?

it is a measure of where the "middle fifty" is in a data set. (Where a range is a measure of where the beginning and end are in a set, an interquartile range is a measure of where the bulk of the values lie; 50th percentile)

What are the the two most common measures of dispersion ?

the range; the standard deviation

Mode

the value that occurs most often in the data

The range attempts to

show how much variation or dispersion from the average exists. The range is the difference between the highest data value and the lowest data value. ( A low range value indicates that the data points tend to be very close to the mean; a high range value indicates that the data points are spread out over a large range of values.)