Zero is a value, blank is not
A score of 0 counts in the mean. A match not played does not.
Zero or nothing?
A player’s runs in a series of 7 matches are: 57, 13, 0, 84, —, 51, 27. In Match 3 the player played and scored 0. In Match 5 the player did not play (—).
To find the mean runs per match, by how many should we divide the total?
What this lesson covers
The idea
When finding a mean, a recorded value of 0 counts as a data value, but a missing value, where nothing was observed, is left out of the number of values.
Zero or nothing?
A player’s runs in a series of 7 matches are: 57, 13, 0, 84, —, 51, 27. In Match 3 the player played and scored 0. In Match 5 the player did not play (—).
To find the mean runs per match, by how many should we divide the total?
- 6, because Match 5 was not played
- 7, because there are 7 matches
- It does not matter
Count the matches played
Sort each match: does it count in the mean, or is it left out? The toy works out the mean from the matches you counted.
0 is something; blank is nothing
A score of 0 was observed. The player played and made no runs, so it is a data value and it counts. Match 5 has no value, because nothing was observed. So the number of matches is 6, not 7.
The mean is (57 + 13 + 0 + 84 + 51 + 27) ÷ 6 = 232 ÷ 6 = 38.7 runs per match.
When finding a mean, a recorded value of 0 counts as a data value, but a missing value, where nothing was observed, is left out of the number of values.
- Match | Runs | Counts?
- Match 3 | 0 | Yes
- Match 5 | not played | No
Notes
When finding a mean, a recorded value of 0 counts as a data value, but a missing value, where nothing was observed, is left out of the number of values.
Check yourself
Find the mean runs per match of 57, 13, 0, 84, 51 and 27, correct to 1 decimal place.
Answer: 38.7 runs
232 ÷ 6 = 38.66…, which is 38.7 runs per match.
Why do we divide by 6 and not by 7?
A player scored 4, 0 and 20 in three matches. He was injured for a fourth match and could not play. What is his mean score per match played?
Answer: 8
(4 + 0 + 20) ÷ 3 = 24 ÷ 3 = 8.
Sita’s mango tree gave 0, 0, 8, 24, 41, 16, 5, 0, 0, 0, 0, 0 mangoes in the 12 months of a year. To find the mean per month for the mango season, which months should we use?
- Match 5 was not played, so there is no value for it. — correct. Yes! A value that was never observed is left out of the count.
- Because the player scored 0 in Match 3.. A score of 0 is a real value and is counted. That is why Match 3 is among the 6.
- Because 7 is too big a number.. The size of 7 is not the reason. Only the matches with a recorded score are counted.
- All 12 months, including the zeros. That gives 94 ÷ 12 = 7.8, which is much lower than a mango month really is.
- Only the 5 summer months when mangoes are expected to grow: 8, 24, 41, 16, 5 — correct. Yes! Out of season, no mangoes are expected. The mean for the season is 94 ÷ 5 = 18.8.
- Only the months with 0 mangoes. The zero months say nothing about the season. We want the months when mangoes grow.