Question

following distribution shows the marks obtained by a class of hundred student mark 10 to 20 20 to 30 30 to 40 40 to 50 50 60 60 to 70 frequency 10:15 30328 V draw an ogive less than ogive find out median from it ​

Answer 1

Answer:

median = 38

Given:-

$\: c \: .i \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: frequency \\ 10 - 20 \: \: \: \: \: \: \: \: \: \: \: \: \: 10 \\ 20 - 30 \: \: \: \: \: \: \: \: \: \: \: \: \: 15 \\ 30 - 40 \: \: \: \: \: \: \: \: \: \: \: \: \: 30 \\ 40 - 50 \: \: \: \: \: \: \: \: \: \: \: \: \: 32 \\ 50 - 60 \: \: \: \: \: \: \: \: \: \: \: \: \: 8 \\ 60 - 70 \: \: \: \: \: \: \: \: \: \: \: \: \: \: 5$

To find:-

1. ogive
2. meadian

solution:-

$\: c \: .i \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: frequency \: \: \: \: \: \: \: c \: .f \\ 10 - 20 \: \: \: \: \: \: \: \: \: \: \: \: \: 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 10 \\ 20 - 30 \: \: \: \: \: \: \: \: \: \: \: \: \: 15 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 25\\ 30 - 40 \: \: \: \: \: \: \: \: \: \: \: \: \: 30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 55 \\ 40 - 50 \: \: \: \: \: \: \: \: \: \: \: \: \: 32 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 87 \\ 50 - 60 \: \: \: \: \: \: \: \: \: \: \: \: \: 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 95\\ 60 - 70 \: \: \: \: \: \: \: \: \: \: \: \: \: \: 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 100 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Σ \: f \: = 100$

• using the given data construct a cumulative frequency table as shown in picture .on a graph paper ,marks class interval ( c. i) along x axis and cumulative frequency along Y axis.
• on this graph mark point
• ( 20 , 10) (30 , 25) (40 , 55) (50 , 87)(60,95)(70, 100)
• then draw a free hand curve passing throgh tge point marked, stating from the lower limits of the first class and terminating at upper limit of the last class .the curve so obtain is o give as shown in picture plz refer the picture

$since \\ the \: no \: of \: term \: \: = 100 \\ \\ meadian = ( \frac{n}{2} )th \: \: \: term \\ \\ meadian = \frac{100}{2} th \: \: term \\ \\ median = 50th \: term \:$

• throught mark 50 on y axis ,draw a horizontal line which line mark meer the curve at point A.
• throght A on the curve draw a vertical line whicch meet x axis at the point B
• the value of B on x axis is median

meadian = 38