Mathematics, 16.09.2019 02:30 marianabeel230

The following table 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
part a: create a five-number summary and calculate the interquartile range for the two sets of data. (6 points)
part b: are the box plots symmetric? justify your answer. (4 points)

Answers: 2

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Answer from: doritasanchez

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.

Answer from: Quest

We need the pictures of the graphs

Answer from: Quest

false

step-by-step explanation:

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