Question

If the mean of the following data is 53 find x Class frequency 0-20. 12
20-40. 15
40-60. 32
60-80. X
80-100. 13

Answer 1

$\bf \: \: 0 - 20 \: \: \: \longrightarrow \: \: 12 \\ \bf20 - 40 \: \: \: \longrightarrow \: \:15 \\ \bf 40 - 60 \: \: \: \longrightarrow \: \: 32 \\ \bf 60 - 80 \: \: \: \longrightarrow \: \: x \\ \bf 80 - 100 \: \: \: \longrightarrow \: \: 13$

Now,

$\sf \bar{x} \rightarrow \frac{(12)20 + (15)20 +(32)20 + (x)20 + (13)20 }{100} \\ \\ \rm{ \: \: \: = > \frac{240 + 300 + 640 + 20x + 260}{100} = 53} \\ \\ \tt{\: \: \: = > \frac{1440 + 20x}{100} = 53 } \\ \\ \bf \: \: \: = > 1440 + 20x = 5300 \\ \sf \: \: \: = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 20x = 5300 - 1440 \\ \rm \: \: \: = > \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{386 \cancel0}{2 \cancel0} = \red{193}$