The following table shows the number of males (M) and females (F), in…
2023
The following table shows the number of males (M) and females (F), in thousands, in Towns X and Y from 2018 to 2022.
Year | Town X — males | Town X — females | Town Y — males | Town Y — females |
|---|---|---|---|---|
2018 | 50 | 49 | 53 | 50 |
2019 | 52 | 49 | 54 | 52 |
2020 | 55 | 52 | 55 | 54 |
2021 | 53 | 53 | 58 | 56 |
2022 | 55 | 52 | 62 | 55 |
For each town, find the number of years in which its female count is below that town’s average female count. Report the result as the ordered pair (Town X, Town Y).
Answer: B. Two, Two — ConceptFor a list of n observations, the arithmetic mean is the sum of all observations divided by n. To count observations below the mean, compute the mean…
- A.
One, two
- B.
Two, Two
- C.
Three, Two
- D.
Two, one
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Concept
For a list of n observations, the arithmetic mean is the sum of all observations divided by n.
To count observations below the mean, compute the mean for each data series separately and compare every observation with its own series mean.
Application
For Town X females, the total is 49 + 49 + 52 + 53 + 52 = 255 thousand, so the average is 255 / 5 = 51 thousand.
The Town X female counts below 51 thousand are 49 thousand in 2018 and 49 thousand in 2019. Hence the count is 2 years.
For Town Y females, the total is 50 + 52 + 54 + 56 + 55 = 267 thousand, so the average is 267 / 5 = 53.4 thousand.
The Town Y female counts below 53.4 thousand are 50 thousand in 2018 and 52 thousand in 2019. Hence the count is 2 years.
Cross-check
Town | Average female count (thousand) | Years below average | Count |
|---|---|---|---|
X | 51 | 2018, 2019 | 2 |
Y | 53.4 | 2018, 2019 | 2 |
Therefore, the required pair is Two, two.