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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.
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.
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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 Mark)
(ii) Air Quality is poor on most of the days (1 Mark)
(iii) (a) Modal class is 200.5 - 300.5 (1/2 Mark)
Mode = $200.5 + 100 (\frac{12-9}{2\times12-9-4})$ (1/2 Mark)
$= 227.77$ (1 Mark)
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 1/2 Mark)
Median class is 200.5 - 300.5 (1 Mark)
Median = $200.5 + (\frac{15-12}{12}) \times 100$ (1/2 Mark)
$= 225.5$ (1 Mark)
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 Mark)
(ii) Air Quality is poor on most of the days (1 Mark)
(iii) (a) Modal class is 200.5 - 300.5 (1/2 Mark)
Mode = $200.5 + 100 (\frac{12-9}{2\times12-9-4})$ (1/2 Mark)
$= 227.77$ (1 Mark)
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 1/2 Mark)
Median class is 200.5 - 300.5 (1 Mark)
Median = $200.5 + (\frac{15-12}{12}) \times 100$ (1/2 Mark)
$= 225.5$ (1 Mark)