Question

2. Using the histogram above, determine the grade students scored with the highest frequency.

a. 60-70
b. 70-80
c. 80-90
d. 90-100

3. The box-and-whisker plot shows the range of work commutes for New York City workers. What percentage of workers commute 35 minutes or more to work?
a. 100%
b. 75%
c. 50%
d. 25%

5. Find the first quartile and the third quartile for the set of values.
36, 38, 42, 47, 51, 56, 62, 69, 70, 74
a. first quartile = 36, third quartile= 74
b. first quartile = 51, third quartile = 56
c. first quartile = 38, third quartile= 70
d. first quartile = 42, third quartile = 69

6. Below is a box-and-whisker plot that displays the scores from a chapter test.
Which percentage of students scored between 88 and 96.
a. 75%
b. 50%
c. 25%
d. 0%

Answer 1

(2) The correct option is c. (3) The correct option is b. (5) The correct option is d. (6) The correct option is c.

Explanation:

(2)

In the first figure 1, x-axis represents marks and y-axis represents the number of students or frequency.

From the given figure it is noticed that peak of the graph is 13 at 80-90.

Therefore correct option is c.

(3)

In a box plot left and right sides of the box represents Q₁ and Q₃ respectively. The line insides the box represents the median.

The lines extend from the left and right of the box to the adjacent values. These adjacent values are lower and upper limits of the data. The left adjacent value is known as lower limit and right adjacent value is known as upper limit.

`Q_1=25\%`

`Q_2=50\%`

`Q_3=75\%`

From the second figure it is noticed the 35 is the first quartile, it means 25% workers commute less than 35 minutes to work and 75% workers commute 35 minutes or more to work.

Therefore correct option is b.

(5)

Total number of observation is 10, which is an even number.

`Q_1=(n)/(4)\text{th term}=(10)/(4)=2.5=3\text{th term}`

Therefore Q₁ is the 3 term of the data. i.e 42.

`Q_3=(3n)/(4)\text{th term}=(3* 10)/(4)=7.5=8\text{th term}`

Therefore Q₃ is the 8 term of the data. i.e 69.

Therefore correct option is d.

(6)

From the third figure it is notice that 88 is the median and 96 is third quartile of the data.

We know that
`Q_2=50\%` and
`Q_3=75\%`

Therefore the data between median and Q₃ is

`Q_3-Q_2=75\%-50\%=25\%`

Therefore correct option is c.