Question

The following table shows the number of hours some students in two universities spend reading each week:

Answer 1

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, $Q_1$, 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:

$Q_1= \frac{2+3}{2}=\frac{5}{2}=2.5$

Similarly, the upper half of the data is: {10,14,17,22}, so

$Q_3= \frac{14+17}{2}=\frac{31}{2}=15.5$

→Similarly for School B

The median is 16.

Therefore, the lower half of the data is: {9,10,14,15}.

The first quartile,  $Q_1$, 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:

$Q_1= \frac{10+14}{2}=\frac{24}{2}=12$

Similarly, the upper half of the data is: {17,18,18,20}, so

$Q_3= \frac{18+18}{2}=\frac{36}{2}=18$

Inter quartile range is $IQR=Q_3-Q_1$

                            School A         School B

minimum                 2                  9

$Q_1$        2.5               12

median                    10                16

$Q_3$       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 $Q_1$ and  $Q_3$should be equal for the box plot to be symmetric.