Respuesta :
Answer:
B. 21, 28, 33, 41, 81
Step-by-step explanation:
Data : 21, 22, 22, 24, 24, 24, 24, 25, 26, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 31, 31, 31, 32, 32, 33, 33, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 37, 37, 37, 37, 38, 38, 38, 39, 39, 39, 41, 41, 41, 41, 42, 42, 44, 45, 45, 45, 47, 49, 49, 54, 60, 60, 61, 61, 61, 62, 62, 74, 81
Five number summary includes :
1. Minimum vale
2. First Quartile
3. Median : mid value of the given data is 46th term = 33
4.Third Quartile
5.Maximum value
Solution :
1. Minimum vale : smallest value of data = 21
2. First Quartile: median of the data (first number to the actual median) i.e. from 1st term to 46th term
Median for even number of terms : [tex]\frac{\frac{n}{2}th+(\frac{n}{2}+1)th}{2}[/tex]
n = 46
so, median = [tex]\frac{\frac{46}{2}th+(\frac{46}{2}+1)th}{2}[/tex]
= [tex]\frac{23th+24th}{2}[/tex]
= [tex]\frac{28+28}{2}[/tex]
= [tex]\frac{56}{2}[/tex]
= [tex]28[/tex]
Thus first quartile = 28
3. Median : mid value of the given data(ages of 91 women) is 46th term = 33
4.Third Quartile :median of the data (46th number[actual median] to the 91th)
Median for even number of terms : [tex]\frac{\frac{n}{2}th+(\frac{n}{2}+1)th}{2}[/tex]
n = 46
so, median = [tex]\frac{\frac{46}{2}th+(\frac{46}{2}+1)th}{2}[/tex]
= [tex]\frac{23th+24th}{2}[/tex]
= [tex]\frac{41+41}{2}[/tex]
= [tex]\frac{82}{2}[/tex]
= [tex]41[/tex]
Thus third quartile = 41
5.Maximum value : highest value of data = 81
Thus the five number summary is 21, 28, 33, 41, 81
Hence Option B is correct
