The Heights of 29 children are given in the table below :
Heights(in ft.)No. of children2.5−353−3.563.5−474−4.594.5−52
What is the median height of the children?
The Heights of 29 children are given in the table below :
Heights(in ft.)No. of children2.5−353−3.563.5−474−4.594.5−52
What is the median height of the children?
The correct option is C: 3.75 ft
Lets form the cumulative frequency table to evaluate the median,
C.IFrequency~(f)Cumulative Frequency~(cf)2.5−3553−3.565+6=11 (cf)(L) 3.5−47 (F)5+6+11=184−4.595+6+11+9=274.5−525+6+11+9+2=29N=29
Here, total no. of children =N=29 (An odd number)
Median = ((29+1)2)th observation =15th th observation.
It will come after 11 in cumulative frequency.
So, the Median class is 3.5−4.. and
Lower boundary L=3.5
Corresponding frequency (F)=7
Corresponding preceding cumulative frequency (cf)=11
Size of the class interval (h)=4−3.5=0.5=510=12
Now, the Median =L+(N2−cfF)×h
=3.5+(292−11)7×12
=3.5+(29−22)2×7×12
=3.5+72×7×12
=3.5+14
=3.5+0.25
=3.75
Therefore, median height of the children is 3.75 ft.
The correct option is C: 3.75 ft
Lets form the cumulative frequency table to evaluate the median,
C.IFrequency~(f)Cumulative Frequency~(cf)2.5−3553−3.565+6=11 (cf)(L) 3.5−47 (F)5+6+11=184−4.595+6+11+9=274.5−525+6+11+9+2=29N=29
Here, total no. of children =N=29 (An odd number)
Median = ((29+1)2)th observation =15th th observation.
It will come after 11 in cumulative frequency.
So, the Median class is 3.5−4.. and
Lower boundary L=3.5
Corresponding frequency (F)=7
Corresponding preceding cumulative frequency (cf)=11
Size of the class interval (h)=4−3.5=0.5=510=12
Now, the Median =L+(N2−cfF)×h
=3.5+(292−11)7×12
=3.5+(29−22)2×7×12
=3.5+72×7×12
=3.5+14
=3.5+0.25
=3.75
Therefore, median height of the children is 3.75 ft.
