Birthdays/stats

This page collects some statistics on the listed Birthdays of MCO.

Summary Statistics

Basic summary statistics (off R): Minimum, 1st Quartile, Median, Mean, 3rd Quartile and Maximum for birthdays per day (with all days in a leap year being considered) and per month.

Birthdays:	Min.	1st Qu.	Median	Mean	3rd Qu.	Max.
per day	0	0	1	0.88	1.00	6
per month	19	24	26	26.92	30.50	36

• Boxplots for the data
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  Maximum is outlier.

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Question: Do the listed birthdays of MCO occur with an equal probability for each month in the year?

Answer

Yes.

Method

A chi squared (χ²) test was used to test this hypothesis.

• H₀ : birthdays did occur with equal probability (month-wise); p_Jan = p_Feb = ... = p_Dec = 1/12.
• H₁ : H₀ is false.

Testing at α = 0.05 (p = 0.95) and with the degrees of freedom being 11 (number of months minus one), the critical χ² value is 19.68 (https://www.itl.nist.gov/div898/handbook/eda/section3/eda3674.htm).

Table of raw data (month and observed number of birthdays) and calculated data (anything with 2 decimal places).

month	o(bserved)	e(xpected)	o-e	(o-e)^2	[(o-e)^2]/e
1	28	26.92	1.08	1.17	0.04
2	24	26.92	-2.92	8.51	0.32
3	32	26.92	5.08	25.84	0.96
4	30	26.92	3.08	9.51	0.35
5	24	26.92	-2.92	8.51	0.32
6	24	26.92	-2.92	8.51	0.32
7	36	26.92	9.08	82.51	3.07
8	28	26.92	1.08	1.17	0.04
9	22	26.92	-4.92	24.17	0.90
10	24	26.92	-2.92	8.51	0.32
11	19	26.92	-7.92	62.67	2.33
12	32	26.92	5.08	25.84	0.96
TOTAL	323				9.92

The calculated χ² was 9.92, which is lower than the critical χ², so H₀ cannot be rejected when α = 0.05.