Stats Week 2 - Data Displays, Descriptive Statistics, and Graphs

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Q1

25th percentile= "median" of lower half

Q2

50th percentile= median

Q3

75th percentile = median of the upper half of the data

In a boxplot you can tell the exact pattern of the data set (beyond just whether the data is skewed or symmetric.)

False

The median must be one of the numbers in the data set.

False

The standard deviation has no units.

False

A flat histogram (with a line straight across) contains no variability whatsoever, according to our definition.

False (has more variability)

The slices on a pie chart represent relative frequencies.

True

The starting point can affect the way a graph looks.

True

What is the 5 number summary?

min, Q1, median, Q3, max

Which type of graph is best for COMPARING two or more quantitative data sets, a boxplot or a histogram?

Boxplot

Which type of graph is made from the 5-number summary?

Boxplot

Categorical Data

Data that consists of names, labels, or other nonnumerical values

A listing of all possible values in a data set and how often they occurred is called a data _____________________.

Distribution

If the mean of a data set is large, the standard deviation has to be large also.

False

Data Distribution

List of all data values and how often they occur

Center

Mean and the median, *don't have to be a value in the data set*

more variability vs. less variability

More has the same amount far away as is close (the same size all around). While less is more concentrated in the middle (goes up then down).

Frequencies

Number in each category - Table Bar graph showing # in each category

Which is more affected by skewness, the IQR or standard deviation?

Standard Deviation

As we heard in lecture, the "average distance from the mean" is measured by the __________________________.

Standard deviation

Boxplot A and Boxplot B are drawn on the same axes. The box part of Boxplot A is shorter in length than the box part of Boxplot B. What can you tell about the two data sets?

You cannot tell anything from the information provided.

Skewed left

mean < median

Symmetric Data

mean = median

relative frequency

the fraction or percent of the time that an event occurs in an experiment -table, pie chart - bar graph showing % in each category

Variables

Any measurable conditions, events, characteristics, or behaviors that are controlled or observed in a study.

What is the standard deviation of the data set 1, 1, 1, 1?

0

If you add 10 to every value of a data set, what happens to the standard deviation?

Stays the same

If a data set is skewed to the left, how will the mean and median compare?

The mean will be less than the median.

Variability

how the data are dispersed or spread around the mean/center - standard deviation, quartiles

IQR

interquartile range (Q3-Q1)

What can never be negative

standard deviation

Boxplot

- A graph of the five-number summary -Special area around Q1 to Q3 to indicate middle 50% of the data - Can immediately see median, IQR, and skewness - You are interested in how concentrated the data are within each other - Can't see the mean and sample size - Easy to compare data sets

An outlier in a data set can significantly affect the value of the mean but not the median.

True

You can have two data sets with the same mean but different standard deviations.

True

Standard deviation

a computed measure of how much scores vary around the mean score - Same units as the original data - Never negative - Can = 0 - Is affected by outliers and skewness

Histograms

- Nice way to see shape of data set - Hard to identify quartiles - Rough idea of center or variability - Hard to compare data sets

Suppose your data represent revenues from a group of 20 stores in a retail chain across the country, and revenue is measured in millions of dollars. The standard deviation of this data set would also be measured in millions of dollars.

True

Quantitative Data

measurements and counts

Skewed right

mean > median


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