A survey regarding the heights (in cm) of 51 girls of Class X of a school was conducted and data was obtained as shown in table. Find their median.
Height (in cm) Number of girls
Less than 140 4
Less than 145 11
Less than 150 29
Less than 155 40
Less than 160 46
Less than 165 51
Answers
Answer:
Step-by-step explanation:
Cumulative frequency = n = 51
and n/2 = 25.5
Since, the cumulative frequency greater than 25.5 is 29 on the corresponding class of 145 - 150, thus 145 - 150 is the median class.
Where, l = 145 , f =18 , h = 5 and c.f = 11
Median = l + [(n/2 - cf )/f ] ×h
Where, l is the lower limit of the median class, n is the number of observations , cf is the cumulative frequency of class interval preceding the median class, f is the frequency of median class and h is the class size
Thus,
= 145 + [25.5 - 11)/18] × 5
= 145 + (14.5)/18 ×5
= 145 + 72.5/18
= 145 + 4.03
= 149.03
Hence, the median height of girls is 149.03 cm.
Answer:
Step-by-step explanation:
Cumulative frequency = n = 51
and n/2 = 25.5
Since, the cumulative frequency greater than 25.5 is 29 on the corresponding class of 145 - 150, thus 145 - 150 is the median class.
Where, l = 145 , f =18 , h = 5 and c.f = 11
Median = l + [(n/2 - cf )/f ] ×h
Where, l is the lower limit of the median class, n is the number of observations , cf is the cumulative frequency of class interval preceding the median class, f is the frequency of median class and h is the class size
Thus,
= 145 + [25.5 - 11)/18] × 5
= 145 + (14.5)/18 ×5
= 145 + 72.5/18
= 145 + 4.03
= 149.03
Hence, the median height of girls is 149.03 cm.