Question 3
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.
Daily pocket allowance (in Rs)11−1313−1515−1717−1919−2121−2323−25Number of workers76913f54
Question 3
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.
Daily pocket allowance (in Rs)11−1313−1515−1717−1919−2121−2323−25Number of workers76913f54
We may find class mark xi for each interval by using the relation:
xi =Upper class limit + lower class limit2
Given that mean pocket allowance xi = Rs.18
Now taking 18 as assured mean a we may calculate di and fidi as following.
Daily pocket allowance (in Rs)Number of workers fiClass mark xidi=xi−18fidi11−13712−6−4213−15614−4−2415−17916−2−1817−1913180019−21f2022f21−2352242023−25424624Total∑fi=44+f 2f−40
From the table we may obtain:
∑fi=44+f∑fiui=2f−40¯x=a+∑fidi∑fi18=18+(2f−4044+f)2f−40=02f=40f=20
Hence, the missing frequency 'f' is 20.
We may find class mark xi for each interval by using the relation:
xi =Upper class limit + lower class limit2
Given that mean pocket allowance xi = Rs.18
Now taking 18 as assured mean a we may calculate di and fidi as following.
Daily pocket allowance (in Rs)Number of workers fiClass mark xidi=xi−18fidi11−13712−6−4213−15614−4−2415−17916−2−1817−1913180019−21f2022f21−2352242023−25424624Total∑fi=44+f 2f−40
From the table we may obtain:
∑fi=44+f∑fiui=2f−40¯x=a+∑fidi∑fi18=18+(2f−4044+f)2f−40=02f=40f=20
Hence, the missing frequency 'f' is 20.
