63
CENTRAL POLLUTION CONTROL BOARD'S
AIR QUALITY STANDARDS
AIR QUALITY INDEX (AQI)
CATEGORY
0-50
Good
51-100
Satisfactory
101-200
Moderate
201-300
Poor
301-400
Very Poor
401-500
Severe
The Air Quality Index (AQI) is a scale from $0$ to $500$ that indicates air quality, with higher numbers signifying more pollution and greater health concerns.
Mansi collected the daily data of AQI of her city for a month and presented it as given below:
AQI Range :
1-100 101-200 201-300 301-400 401-500
Number of Days: $3$ $9$ $12$ $4$ $2$
(i) Convert the data to continuous frequency distribution.
(ii) What is the quality of air in most of the days of the month ?
(iii) (a) Using table formed in part (i), find mode of the data.
OR
(b) Using table formed in part (i), find median of the data.
AIR QUALITY STANDARDS
AIR QUALITY INDEX (AQI)
CATEGORY
0-50
Good
51-100
Satisfactory
101-200
Moderate
201-300
Poor
301-400
Very Poor
401-500
Severe
The Air Quality Index (AQI) is a scale from $0$ to $500$ that indicates air quality, with higher numbers signifying more pollution and greater health concerns.
Mansi collected the daily data of AQI of her city for a month and presented it as given below:
AQI Range :
1-100 101-200 201-300 301-400 401-500
Number of Days: $3$ $9$ $12$ $4$ $2$
(i) Convert the data to continuous frequency distribution.
(ii) What is the quality of air in most of the days of the month ?
(iii) (a) Using table formed in part (i), find mode of the data.
OR
(b) Using table formed in part (i), find median of the data.
Show SolutionHide Solution↓
Solution: (i)
Class Interval
frequency
0.5-100.5
3
100.5 - 200.5
9
200.5 - 300.5
12
300.5-400.5
4
400.5-500.5
2 (1)
(ii) Air Quality is poor on most of the days (1)
(iii) (a) Modal class is $200.5 - 300.5$ (
frac{1}{2})
Mode = $200.5 + 100 (\frac{12-9}{2\times 12-9-4})$ (1)
$= 227.77$ (
frac{1}{2})
OR
(b)
Class Interval
frequency
cf
0.5-100.5
3
3
100.5 - 200.5
9
12
200.5 - 300.5
12
24
300.5-400.5
4
28
400.5-500.5
2
30
For correct table (
frac{1}{2})
Median class is $200.5 - 300.5$ (
frac{1}{2})
Median = $200.5 + (\frac{15-12}{12}) \times 100$ (1)
$= 225.5$ (
frac{1}{2})
Class Interval
frequency
0.5-100.5
3
100.5 - 200.5
9
200.5 - 300.5
12
300.5-400.5
4
400.5-500.5
2 (1)
(ii) Air Quality is poor on most of the days (1)
(iii) (a) Modal class is $200.5 - 300.5$ (
frac{1}{2})
Mode = $200.5 + 100 (\frac{12-9}{2\times 12-9-4})$ (1)
$= 227.77$ (
frac{1}{2})
OR
(b)
Class Interval
frequency
cf
0.5-100.5
3
3
100.5 - 200.5
9
12
200.5 - 300.5
12
24
300.5-400.5
4
28
400.5-500.5
2
30
For correct table (
frac{1}{2})
Median class is $200.5 - 300.5$ (
frac{1}{2})
Median = $200.5 + (\frac{15-12}{12}) \times 100$ (1)
$= 225.5$ (
frac{1}{2})