Respuesta :
Answer:
The median number of shoes for the girls is greater than the median number of shoes for the boys.
Step-by-step explanation:
Jeffrey surveys the 13 girls and 13 boys in his class to find out how many pairs of shoes they have in their closets
Girls Data :10, 12, 9 , 15, 25,8, 6,14, 18 , 11 , 9 , 13 , 15
Arrange the data in the ascending order :
6,8,9,9,10,11,12,13,14,15,15,18,25
No. of observations n = 13(odd)
So, Median = [tex](\frac{n+1}{2})^{\text{th term}}[/tex]
= [tex](\frac{13+1}{2})^{\text{th term}}[/tex]
= [tex](\frac{14}{2})^{\text{th term}}[/tex]
= [tex](7)^{\text{th term}}[/tex]
= [tex]12[/tex]
Thus the median of the girls data is 12.
Now to find [tex]Q_3[/tex]
Consider the set of values right to the median .
13,14,15,15,18,25
Now find the median of this data
No. of observations n = 6(even)
Median = [tex]\frac{(\frac{n}{2}+1)^{\text{th term}}+\frac{n}{2}^{\text{th term}}}{2}[/tex]
So, Median = [tex]\frac{(\frac{6}{2}+1)^{\text{th term}}+\frac{6}{2}^{\text{th term}}}{2}[/tex]
Median = [tex]\frac{4^{\text{th term}}+3^{\text{rd term}}}{2}[/tex]
Median = [tex]\frac{15+15}{2}[/tex]
Median = [tex]15[/tex]
Mean = [tex]\frac{\text{Sum of all observations }}{\text{number of observations}}[/tex]
Mean = [tex]\frac{10+12+ 9 +15+25+8+6+14+18+ 11 +9+ 13+15}{13}[/tex]
Mean = [tex]12.69[/tex]
So, [tex]Q_3[/tex] for girls is 15 and median is 12 and mean is 12.6.
Boys data : 8,6,4,5,10,15,7,8,12,11,9,5,4
Arrange the data in the ascending order :
4,4,5,5,6,7,8,8,9,10,11,12,15
No. of observations n = 13(odd)
So, Median = [tex](\frac{n+1}{2})^{\text{th term}}[/tex]
= [tex](\frac{13+1}{2})^{\text{th term}}[/tex]
= [tex](\frac{14}{2})^{\text{th term}}[/tex]
= [tex](7)^{\text{th term}}[/tex]
= [tex]8[/tex]
Thus the median of the boys data is 8
Now to find [tex]Q_3[/tex]
Consider the set of values right to the median .
8,9,10,11,12,15
Now find the median of this data
No. of observations n = 6(even)
Median = [tex]\frac{(\frac{n}{2}+1)^{\text{th term}}+\frac{n}{2}^{\text{th term}}}{2}[/tex]
So, Median = [tex]\frac{(\frac{6}{2}+1)^{\text{th term}}+\frac{6}{2}^{\text{th term}}}{2}[/tex]
Median = [tex]\frac{4^{\text{th term}}+3^{\text{rd term}}}{2}[/tex]
Median = [tex]\frac{11+10}{2}[/tex]
Median = [tex]10.5[/tex]
Mean = [tex]\frac{\text{Sum of all observations }}{\text{number of observations}}[/tex]
Mean = [tex]\frac{4+4+5+5+6+7+8+8+9+10+11+12+15}{13}[/tex]
Mean = [tex]8[/tex]
So, [tex]Q_3[/tex] for boys is 10.3 and median is 8 and mean is 8
Since we can see that the value of [tex]Q_3[/tex] , mean and median opf girls is greater than boys.
So, Option C is correct.
The median number of shoes for the girls is greater than the median number of shoes for the boys.
