Question

The ages of students enrolled in two math classes at the local community college, Class A and Class B, are listed in order below. Determine which of the following statements is true about Class B.

Class A: 20, 20, 20, 21, 22, 23, 23, 25, 27, 29, 30, 31, 34, 35, 36, 39, 40
Class B: 16, 17, 18, 18, 20, 22, 22, 24, 26, 26, 28, 29, 30, 34, 37, 40, 42

Class B has a smaller median and the same interquartile range.

Class B has a larger median and the same interquartile range.

Class B has a larger median and a larger interquartile range.

Class B has a smaller median and a larger interquartile range.

Answer 1

the person above me is correct

ergt

tget

d

Step-by-step explanation: If u made it this far the nur sure to ace ur next test....

Answer 2

The true statement about Class B is that Class B has a smaller median and the same inter quartile range.

Explanation:

We are given the ages of students enrolled in two math classes at the local community college, Class A and Class B, below;

Class A: 20, 20, 20, 21, 22, 23, 23, 25, 27, 29, 30, 31, 34, 35, 36, 39, 40

Class B: 16, 17, 18, 18, 20, 22, 22, 24, 26, 26, 28, 29, 30, 34, 37, 40, 42

1) Firstly, we will calculate Median for Class A;

For calculating median, first we have to observe that number of observations (n) in our data is even or odd, that is;

• If n is odd, then the formula for calculating median is given by;

Median =
`((n+1)/(2))^(th) \text{ obs.}`

• If n is even, then the formula for calculating median is given by;

Median =
`\frac{((n)/(2))^(th) \text{ obs.}+((n)/(2)+1)^(th) \text{ obs.}}{2}`

Here, number of observation is odd, i.e. n = 17.

So, Median =
`((n+1)/(2))^(th) \text{ obs.}`

=
`((17+1)/(2))^(th) \text{ obs.}`

=
`((18)/(2))^(th) \text{ obs.}`

=
`9^(th) \text { obs.}` = 27

Hence, the median of class A is 27.

2) Now, we will calculate Median for Class B;

For calculating median, first we have to observe that number of observations (n) in our data is even or odd, that is;

• If n is odd, then the formula for calculating median is given by;

Median =
`((n+1)/(2))^(th) \text{ obs.}`

• If n is even, then the formula for calculating median is given by;

Median =
`\frac{((n)/(2))^(th) \text{ obs.}+((n)/(2)+1)^(th) \text{ obs.}}{2}`

Here, number of observation is odd, i.e. n = 17.

So, Median =
`((n+1)/(2))^(th) \text{ obs.}`

=
`((17+1)/(2))^(th) \text{ obs.}`

=
`((18)/(2))^(th) \text{ obs.}`

=
`9^(th) \text { obs.}` = 26

Hence, the median of class B is 26.

3) Now, we will calculate the Inter quartile range for Class A;

Inter quartile range = Upper quartile - Lower quartile

=
`Q_3-Q_1`

SO,
`Q_1 = ((n+1)/(4))^(th) \text{ obs.}`

=
`((17+1)/(4))^(th) \text{ obs.}`

=
`((18)/(4))^(th) \text{ obs.}`

=
`4.5^(th) \text{ obs.}`

=
`4^(th) \text{ obs.} + 0.5[5^(th) \text{ obs.} - 4^(th) \text{ obs.}]`

=
`21+ 0.5[22- 21]`

= 21.5

Similarly,
`Q_3 = 3((n+1)/(4))^(th) \text{ obs.}`

=
`3((17+1)/(4))^(th) \text{ obs.}`

=
`((54)/(4))^(th) \text{ obs.}`

=
`13.5^(th) \text{ obs.}`

=
`13^(th) \text{ obs.} + 0.5[14^(th) \text{ obs.} - 13^(th) \text{ obs.}]`

=
`34+ 0.5[35- 34]`

= 34.5

Therefore, Inter quartile range for Class A = 34.5 - 21.5 = 13.

4) Now, we will calculate the Inter quartile range for Class B;

Inter quartile range = Upper quartile - Lower quartile

=
`Q_3-Q_1`

SO,
`Q_1 = ((n+1)/(4))^(th) \text{ obs.}`

=
`((17+1)/(4))^(th) \text{ obs.}`

=
`((18)/(4))^(th) \text{ obs.}`

=
`4.5^(th) \text{ obs.}`

=
`4^(th) \text{ obs.} + 0.5[5^(th) \text{ obs.} - 4^(th) \text{ obs.}]`

=
`18+ 0.5[20- 18]`

= 19

Similarly,
`Q_3 = 3((n+1)/(4))^(th) \text{ obs.}`

=
`3((17+1)/(4))^(th) \text{ obs.}`

=
`((54)/(4))^(th) \text{ obs.}`

=
`13.5^(th) \text{ obs.}`

=
`13^(th) \text{ obs.} + 0.5[14^(th) \text{ obs.} - 13^(th) \text{ obs.}]`

=
`30+ 0.5[34- 30]`

= 32

Therefore, Inter quartile range for Class B = 32 - 19 = 13.

Hence, the true statement about Class B is that Class B has a smaller median and the same inter quartile range.