Read the following scenario and answer the THREE questions that follow.
The plots below depict and compare the average monthly incomes (in Rs. ’000) of males and females in ten cities of India in the years 2005 and 2015. The ten cities, marked A-J in the records, are of different population sizes. For a fair comparison, to adjust for inflation, incomes for both the periods are scaled to 2025 prices. Each red dot represents the average monthly income of females in a particular city in a particular year, while each blue dot represents the average monthly income of males in a particular city in a particular year. The gender gap for a city, for a particular year, is defined as the absolute value of the average monthly income of males, minus the average monthly income of females, in that year.
Q21
DI - Tables & Graphs MULTIPLE CHOICE
Which of the following statements, about the average monthly incomes of the 10 cities, as represented in the plots, is DEFINITELY FALSE?
Answer: B
Readings (Rs. '000, 2025 prices), male / female:
City
2005 M
2005 F
Gap 05
2015 M
2015 F
Gap 15
A
40
27.5
12.5
32.5
25
7.5
B
40
22.5
17.5
32.5
22.5
10
C
35
25
10
30
22.5
7.5
D
32.5
22.5
10
27.5
20
7.5
E
32.5
20
12.5
32.5
25
7.5
F
32.5
17.5
15
32.5
22.5
10
G
32.5
30
2.5
32.5
27.5
5
H
35
20
15
32.5
25
7.5
I
30
20
10
32.5
22.5
10
J
30
22.5
7.5
27.5
22.5
5
Key point: the cities have different populations, so a "combined" average for the 10 cities is a population-weighted average. Its exact value is unknown, but it must lie between the smallest and largest city values.
Option 2: men's 2005 city averages range from 30 to 40. A weighted average cannot fall below 30, so "less than Rs. 30,000" is impossible. Definitely false.
Option 1: gaps range from 2.5 to 17.5 in 2005 and from 5 to 10 in 2015 (simple means 11.25 and 7.75). A lower combined gap in 2015 is possible.
Option 3: men earned more in 2005 in A, B, C, D, H and J, which is 6 of 10 cities. True.
Option 4: women's 2015 values range from 20 to 27.5. A weighted average below 22 is possible if city D dominates, so this is not definitely false.
Option 5: in each year every city's male value exceeds its female value, and the median of the male values (32.5 in both years) exceeds that of the female values (22.5 in both years). True.
Answer: option 2 (men's combined average below Rs. 30,000 in 2005)
