A Review of Basic Statistics

Data

The following 50 values are fake IQ values from 50 randomly selected people from a population:

106, 108, 92, 127, 104, 102, 119, 89, 93, 136, 100, 125, 78, 97, 106, 105, 85, 100, 84, 111, 116, 67, 119, 81, 107, 110, 97, 90, 102, 107, 113, 69, 75, 121, 116, 107, 111, 114, 60, 117, 93, 103, 96, 113, 95, 108, 94, 84, 118, 111

We will use the data to:

• Calculate a summary of the data.
• Calculate the sample standard deviation.
• Make a histogram to visualize the distribution.
• Make a boxplot to visualize the distribution.

Another set of data we will use are fake grades of the 50 people:

B, B, B, B, B, B, C, B, F, B, B, F, C, B, B, B, C, B, C, B, D, C, C, B, A, C, A, B, A, B, B, C, D, B, B, B, C, A, D, C, D, A, B, B, B, B, B, B, C, B

We will use the data to:

• Create a barplot to visualize the distribution of grades.

A third set of data we will use are the (fake) numbers of good friends of the 50 people:

32, 28, 25, 29, 24, 22, 31, 20, 27, 47, 24, 33, 14, 25, 29, 32, 20, 18, 21, 38, 40, 11, 28, 33, 30, 32, 29, 16, 25, 23, 30, 16, 11, 39, 36, 26, 34, 37, 17, 34, 25, 29, 34, 39, 30, 30, 27, 24, 30, 24

We will use the data to:

• Create a scatterplot to see how the number of good friends is related to IQ.

Analysis

The 5-number summary and the mean of IQ data

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    60.0    93.0   104.5   101.6   112.5   136.0

The standard deviation of IQ data

## [1] 15.99986

Histogram

Boxplot

Barplot for Grade Distribution

Scatterplot: Number of Friends vs. IQ

Appendix of R Code

# Prepare IQ data for analysis
IQ <- c(106, 108, 92, 127, 104, 102, 119, 89, 93, 136, 100, 125, 78, 97, 106, 105, 85, 100, 84, 111, 116, 67, 119, 81, 107, 110, 97, 90, 102, 107, 113, 69, 75, 121, 116, 107, 111, 114, 60, 117, 93, 103, 96, 113, 95, 108, 94, 84, 118, 111)

# Create a summary of IQ data
summary(IQ)

# Calculate sample standard deviation for IQ data
sd(IQ)

# Make histogram for IQ data
hist(IQ)

# Make boxplot for IQ data
boxplot(IQ)


# Prepare grade data for analysis
Grade <- c("B", "B", "B", "B", "B", "B", "C", "B", "F", "B", "B", "F", "C", "B", "B", "B", "C", "B", "C", "B", "D", "C", "C", "B", "A", "C", "A", "B", "A", "B", "B", "C", "D", "B", "B", "B", "C", "A", "D", "C", "D", "A", "B", "B", "B", "B", "B", "B", "C", "B")

# Make barplot for grade data. Note: Table the data then plot the table.
barplot(table(Grade))


# Scatterplot: Number of friends (on the y-axis) versus IQ (on the x-axis)

Friend <- c(32, 28, 25, 29, 24, 22, 31, 20, 27, 47, 24, 33, 14, 25, 29, 32, 20, 18, 21, 38, 40, 11, 28, 33, 30, 32, 29, 16, 25, 23, 30, 16, 11, 39, 36, 26, 34, 37, 17, 34, 25, 29, 34, 39, 30, 30, 27, 24, 30, 24)

plot(Friend ~ IQ)