Respuesta :
Answer:
Part A- Interquartile range of school A = 13 and school B= 6
Part B- They are not symmetric.
Step-by-step explanation:
Given : Data that shows the number of hours some students in two universities spend reading each week:
School A : 7 2 3 10 17 14 10 22 2
School B : 9 10 16 18 20 15 17 18 14
To find :
Part A: Create a five-number summary and calculate the inter quartile range for the two sets of data.
Part B: Are the box plots symmetric?
Solution : First arrange the data set in ascending order:
School A: 2, 2, 3, 7, 10, 10, 14, 17, 22
School B: 9, 10, 14, 15, 16, 17, 18, 18, 20
1) Part A - To create five- number summary:
→For School A-
The median is 10.
Therefore, the lower half of the data is: {2,2,3,7}.
The first quartile, [tex]Q_1[/tex], is the median of {2,2,3,7}.
Since there is an even number of values, we need the mean of the middle two values to find the first quartile:
[tex]Q_1= \frac{2+3}{2}=\frac{5}{2}=2.5[/tex]
Similarly, the upper half of the data is: {10,14,17,22}, so
[tex]Q_3= \frac{14+17}{2}=\frac{31}{2}=15.5[/tex]
→Similarly for School B
The median is 16.
Therefore, the lower half of the data is: {9,10,14,15}.
The first quartile, [tex]Q_1[/tex], is the median of {9,10,14,15}.
Since there is an even number of values, we need the mean of the middle two values to find the first quartile:
[tex]Q_1= \frac{10+14}{2}=\frac{24}{2}=12[/tex]
Similarly, the upper half of the data is: {17,18,18,20}, so
[tex]Q_3= \frac{18+18}{2}=\frac{36}{2}=18[/tex]
Inter quartile range is [tex]IQR=Q_3-Q_1[/tex]
School A School B
minimum 2 9
[tex]Q_1[/tex] 2.5 12
median 10 16
[tex]Q_3[/tex] 15.5 18
maximum 22 20
IQR 13 6
2) Part B- The box plot are not symmetric. The distance of the median from each [tex]Q_1[/tex] and [tex]Q_3[/tex]should be equal for the box plot to be symmetric.
