Measures of center

Introduction to Statistics

George Boorman

Curriculum Manager, DataCamp

Why are measures of center useful?

  • Average number of sales orders per month

 

 

  • Typical cost of a house

 

 

  • Most common hair color

shop_window_with_sale_written_on_it.jpg

aerial_shot_of_houses.jpg

brown_hair.jpg

1 Image credits: https://unsplash.com/@arnosenoner; https://unsplash.com/@brenoassis;
Introduction to Statistics

Crime data

Borough Burglary Robbery Theft Vehicle Crime Total
Barking and Dagenham 2318 1265 6300 4668 14551
Barnet 5067 1369 9875 9841 26152
Bexley 1583 444 4500 4216 10743
Brent 3893 1650 10026 7739 23308
Bromley 3053 844 8635 6966 19498
... ... ... ... ... ...
Introduction to Statistics

Crime data

Borough Burglary Robbery Theft Vehicle Crime Total
Barking and Dagenham 2318 1265 6300 4668 14551
Barnet 5067 1369 9875 9841 26152
Bexley 1583 444 4500 4216 10743
Brent 3893 1650 10026 7739 23308
Bromley 3053 844 8635 6966 19498
... ... ... ... ... ...
Introduction to Statistics

Histograms

histogram_of_vehicle_offenses.png

Introduction to Statistics

What is the typical amount of vehicle crime in London?

Where is the center of the data?

  • Mean
  • Median
  • Mode

annotated_vehicle_offenses_histogram_asking_where_the_center_is.png

Introduction to Statistics

Measures of center: mean

 

$${mean} = \frac{Sum\ of\ all\ values}{Count\ of\ all\ values} $$

 

  • Mean burglaries per London borough:

$${Mean(Burglary)} =\frac{(2,318\ + 5,067\ + 1,583\ + 3,893\ +...)}{32} \ = \ 3,462.8125 $$

Introduction to Statistics

Measures of center: mean

Type of Crime Mean
Burglary 3358.06
Robbery 1450.85
Theft 10642.21
Vehicle Offenses 6227.27
Overall 47671.62
Introduction to Statistics

Measures of center: median

  • Median - middle value for a given variable

sorted_bar_plot_showing_burglary_values_by_borough_from_smallest_to_largest.png

Introduction to Statistics

Measures of center: median

 

sorted_bar_plot_showing_burglary_values_by_borough_from_smallest_to_largest_with_values_stated_for_the_two_middle_bars.png

Introduction to Statistics

Measures of center: median

${Median(Burglary)} =\frac{(3,304\ + 3,529)}{2}$

${Median(Burglary)} = 3,416.5 $

Introduction to Statistics

Measures of center: mode

  • Mode - most frequent value
Type of Crime Count
Burglary 110,810
Robbery 47,877
Theft 350,025
Vehicle Offenses 205,337
Introduction to Statistics

Which measure to use?

histogram_of_vehicle_crimes_with_mean_and_median_displayed_as_black_and_red_vertical_dotted_lines.png

Introduction to Statistics

Which measure to use?

robbery_histogram_with_black_dotted_line_for_mean_and_red_dotted_line_for_median.png

Introduction to Statistics

Let's practice!

Introduction to Statistics

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