Measures of center

Introduction to Statistics in R

Maggie Matsui

Content Developer, DataCamp

Mammal sleep data

msleep

# A tibble: 83 x 11
   name             genus       vore  order        sleep_total sleep_rem sleep_cycle awake
   <chr>            <chr>       <chr> <chr>              <dbl>     <dbl>       <dbl> <dbl>
 1 Cheetah          Acinonyx    carni Carnivora           12.1      NA         NA     11.9
 2 Owl monkey       Aotus       omni  Primates            17         1.8       NA      7 
 3 Mountain beaver  Aplodontia  herbi Rodentia            14.4       2.4       NA      9.6
 4 Greater short... Blarina     omni  Soricomorpha        14.9       2.3       0.133   9.1 
 5 Cow              Bos         herbi Artiodactyla         4         0.7       0.667  20  
 6 Three-toed sloth Bradypus    herbi Pilosa              14.4       2.2       0.767   9.6 
 7 Northern fur...  Callorhinus carni Carnivora            8.7       1.4       0.383  15.3 
# ... with 76 more rows, and 2 more variables: brainwt <dbl>, bodywt <dbl>

Histograms

Histogram of mammals' sleep times

How long do mammals in this dataset typically sleep?

What's a typical value?

Where is the center of the data?

Mean
Median
Mode

Histogram with question mark and pointing fingers

Measures of center: mean

  name                       sleep_total
1 Cheetah                           12.1
2 Owl monkey                        17.0 
3 Mountain beaver                   14.4
4 Greater short-tailed shrew        14.9
...

$$\text{Mean sleep time}=\frac{12.1 + 17.0 + 14.4 + 14.9 + ...}{83} = 10.43$$

mean(msleep$sleep_total)

10.43373

Measures of center: median

sort(msleep$sleep_total)

 [1]  1.9  2.7  2.9  3.0  3.1  3.3  3.5  3.8  3.9  4.0  4.4  5.2  5.3  5.3  5.4  5.6  6.2
...
[52] 11.5 12.1 12.5 12.5 12.5 12.5 12.8 12.8 13.0 13.5 13.7 13.8 14.2 14.3 14.4 14.4 14.5
[69] 14.6 14.9 14.9 15.6 15.8 15.8 15.9 16.6 17.0 17.4 18.0 18.1 19.4 19.7 19.9

sort(msleep$sleep_total)[42]

10.1

median(msleep$sleep_total)

10.1

Measures of center: mode

Most frequent value

# Count and sort 'sleep_total' descending
msleep %>% count(sleep_total, sort = TRUE)

   sleep_total     n
         <dbl> <int>
 1        12.5     4
 2        10.1     3
 3         5.3     2
 4         6.3     2
 ...

# Count and sort 'vore' descending
msleep %>% count(vore, sort = TRUE)

  vore        n
  <chr>   <int>
1 herbi      32
2 omni       20
3 carni      19
4 NA          7
5 insecti     5

Filtered Data for Insectivores

msleep %>% 
  filter(vore == "insecti")

  name                  genus        vore    order        sleep_total
  <chr>                 <chr>        <chr>   <chr>              <dbl>
1 Big brown bat         Eptesicus    insecti Chiroptera          19.7
2 Little brown bat      Myotis       insecti Chiroptera          19.9
3 Giant armadillo       Priodontes   insecti Cingulata           18.1
4 Eastern american mole Scalopus     insecti Soricomorpha         8.4

Summary of Sleep Statistics for Insectivores

msleep %>% 
  filter(vore == "insecti") %>%

  summarize(mean_sleep = mean(sleep_total),
           median_sleep = median(sleep_total))

  mean_sleep median_sleep
       <dbl>        <dbl> 
1      16.52         18.9

Adding an outlier

msleep %>% 
  filter(vore == "insecti")

  name                  genus        vore    order        sleep_total
  <chr>                 <chr>        <chr>   <chr>              <dbl>
1 Big brown bat         Eptesicus    insecti Chiroptera          19.7
2 Little brown bat      Myotis       insecti Chiroptera          19.9
3 Giant armadillo       Priodontes   insecti Cingulata           18.1
4 Eastern american mole Scalopus     insecti Soricomorpha         8.4
5 Mystery insectivore   ...          ...     ...                  0.0

Summary statistics after adding an outlier

msleep %>% 
  filter(vore == "insecti") %>%

  summarize(mean_sleep = mean(sleep_total),
           median_sleep = median(sleep_total))

  mean_sleep median_sleep
       <dbl>        <dbl>
1      13.22         18.1

Mean: 16.5 → 13.2

Median: 18.9 → 18.1

Which measure to use?

# Create histogram of insecti
msleep %>% 
  filter(vore == "insecti") %>%
  ggplot(aes(insecti)) +
    geom_histogram()

A histogram with bell-shaped data, and a blue and red line close together in the center of the data. Red represents the mean, blue represents the median.

Skew

Histogram of data with few values on the left, increasing to more values on the right.

Skew

Histogram of data with few values on the left, increasing to more values on the right titled Left-skewed

Skew

Histogram of data with many values on the left, decreasing to few values on the right titled Right-skewed

Which measure to use?

Same histograms from previous slides, but with red and blue lines drawn in for mean and median. On the left skewed data, mean is less than median. On the right skewed data, mean is greater than median.

Let's practice!

Introduction to Statistics in R