Statistical Shorts
Below are some statistical statements. Can you decide whether each is always, sometimes, or never true?
If they are sometimes true, give examples or conditions under which they are true and under which they are false. Are some statements usually true, or almost always true, or almost never true?
If they are always true or never true, give convincing reasons why that is the case.
Be sure to be clear about your statistical assumptions in each case.
1. It is just as likely to rain tomorrow as it is to rain the day after tomorrow.
Usually true as clouds remain over the same area. However, this depends on wind speed and direction. Rain seasons are an example of this as it continuously rains one day after another
2. In a school, there will be two people who share a birthday.
Almost always true as there are usually over 365 people in a school so the chances high. This may not always be true as some schools have few schools e.g. primary schools
3. In a school, it will be someone's birthday every day.
This is sometimes true as in our school with over 1500 pupils, there will an average of 5 people per day.
4. A randomly selected person from London will live to a greater age than a randomly selected person from Calcutta.
Usually true as on average, the living conditions and life expectancy are greater in London than there are in Calcutta. However, the person picked from London may be a smoker, so could live less than a person from Calcutta.
5. If everyone in the class rolled two dice until someone threw a double six, there would be one winner.
Always true as the last roll would be the highest.
6. If I roll a die 100 times, I will get about the same number of 1s as 6s.
Almost always true as the theoretical probability is not the same as the real result. This may be due to the fact that you throw it differently every time or the value is affected by human error.
7. If I flip a fair coin 20 times, I will get 10 heads.
Always true is the theoretical probability, but again, the way you throw it way affect the result.
8. The mean, median and mode of a set of numbers can't all be the same.
Almost never true as they measure different things. The mode measures the most frequent, the median measures the middle figure and the mean measures all the numbers added up then divided by the number of numbers. 2222222222 is an example of where it is true.
9. The mean cannot be less than both the median and the mode.
Almost always true as the median is the middle value and the mode influences the median as it is the most popular.
10. Half of the students taking a test score less than the average mark.
This is only true is the used the median as the mode and mean does not necessarily correspond with the middle man’s mark.
11. Nobody scores higher than the average mark in a test.
This could only happen if everyone got the same mark for median or mode or if the mode is the highest mark. Almost never true.
12. In a game where you can only score an even number of points (0, 2, 10 or 50), the average score over a series of games must be an even number.
Sometimes true as it depends on the number of games. If the number of games is even then the average is also even but if it is odd then it will sometimes be true e.g. 2, 30, 6 will make an odd number.