The following table shows the number of males (M) and females (F) (in thousands) in Towns X and Y during the five years from 2018 to 2022. Based on the data in the table, answer the questions. Year wise numbers of Males and Females in two Towns (in thousands) Years Town X Town Y Number of males Number of females Number of males Number of 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
Find the number of years in which the number of females in Town X and Y is less than their respective average numbers in these two towns.
Two, Two
The question asks us to identify the number of years in which the female population in Town X is less than the average female population of Town X over the five years, and similarly for Town Y. We need to first calculate the average number of females for each town from the provided data table.
Analyzing Town Population Data
Let's look at the given data table showing the female population in thousands for Town X and Town Y from 2018 to 2022.
| Years | Town X | Town Y | ||
|---|---|---|---|---|
| Number of males | Number of females | Number of males | Number of 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 |
Calculating Average Female Population
To find the average number of females for each town, we sum up the number of females for all five years and divide by the number of years (which is 5).
Average Female Population in Town X
The number of females in Town X (in thousands) over the years 2018, 2019, 2020, 2021, and 2022 are 49, 49, 52, 53, and 52 respectively.
Total number of females in Town X over 5 years = $49 + 49 + 52 + 53 + 52 = 255$ thousands.
Average female population in Town X = $\frac{\text{Total females}}{\text{Number of years}} = \frac{255}{5} = 51$ thousands.
Average Female Population in Town Y
The number of females in Town Y (in thousands) over the years 2018, 2019, 2020, 2021, and 2022 are 50, 52, 54, 56, and 55 respectively.
Total number of females in Town Y over 5 years = $50 + 52 + 54 + 56 + 55 = 267$ thousands.
Average female population in Town Y = $\frac{\text{Total females}}{\text{Number of years}} = \frac{267}{5} = 53.4$ thousands.
Comparing Yearly Data to Averages
Now we compare the number of females in each year for Town X and Town Y with their respective average female populations.
Town X: Years with Female Population Less Than Average (51)
- 2018: 49 < 51 (Yes)
- 2019: 49 < 51 (Yes)
- 2020: 52 > 51 (No)
- 2021: 53 > 51 (No)
- 2022: 52 > 51 (No)
The number of years in Town X where the female population is less than the average is 2 (2018 and 2019).
Town Y: Years with Female Population Less Than Average (53.4)
- 2018: 50 < 53.4 (Yes)
- 2019: 52 < 53.4 (Yes)
- 2020: 54 > 53.4 (No)
- 2021: 56 > 53.4 (No)
- 2022: 55 > 53.4 (No)
The number of years in Town Y where the female population is less than the average is 2 (2018 and 2019).
Conclusion
The number of years in which the female population in Town X is less than its average is 2. The number of years in which the female population in Town Y is less than its average is 2.
Therefore, the answer is Two for Town X and Two for Town Y.
Revision Table: Key Calculations
| Town | Sum of Female Population (thousands) | Number of Years | Average Female Population (thousands) | Years Below Average | Count of Years Below Average |
|---|---|---|---|---|---|
| Town X | $49+49+52+53+52=255$ | 5 | $255/5=51$ | 2018, 2019 | 2 |
| Town Y | $50+52+54+56+55=267$ | 5 | $267/5=53.4$ | 2018, 2019 | 2 |
Additional Information: Understanding Averages
The average, or arithmetic mean, is a fundamental concept in statistics used to represent a typical value in a set of numbers. It is calculated by summing all the values in the set and dividing by the total number of values.
In this problem, calculating the average female population helps us find a central value for the female population in each town over the five years. Comparing the yearly population to this average allows us to see which years had a population size that was smaller than the typical level during this period.
Data interpretation questions like this often require calculating averages, percentages, ratios, or differences based on the data presented in tables or graphs. Understanding how to perform these basic calculations is crucial for analyzing data effectively.
Important Questions from Tabulation
The table shows District-wise data of a number of primary school teachers posted in schools of a city.
Study the table and answer the question:
District
Male teachers
Female teachers
East
1650
2375
North
1075
2651
West
1280
1520
South
1170
1085
Central
690
859
What is the difference between the total number of male teachers in the districts East, North, West taken together and the total number of female teachers in the districts East and South?Table shows income (in Rs. ) received by 4 employees of a company during the month of December 2020 and all their income sources.
Source
Amit
Suresh
Nitin
Varun
Salary
35000
38500
29000
42000
Arrears
6000
6300
5000
7500
Bonus
1000
1100
1000
1240
Overtime
1800
1950
1400
1500
What is the ratio of salary of Varun to his income other than salary?Study the table and answer the question:
Income (Rs.)
No. of persons
Less than 200
12
Less than 250
26
Less than 300
34
Less than 350
40
Less than 400
50
What is the percentage of persons earning Rs. 250 or more?The following table shows the annual profit of a company (in Rs. lakh).
2014-2015
2015-2016
2016-0217
2017-2018
2018-2019
625
690
725
775
815
The period which has the maximum percentage increase in profit over the previous year is:
The table given below shows the number of persons participating in a survey from 6 different states.
States Persons S1 100 S2 200 S3 400 S4 500 S5 600 S6 800 What is the ratio of number of person participating in a survey from state S3 to the number of person participating in a survey from state S4?
