**Answer:**

(a) The outlier in the data is **$810**.

(b) The distribution of money spent on textbooks for the 34 students is **right skewed**.

**Step-by-step explanation:**

The data provided for the amount of money 34 college students spent on books is:

S = {120, 130, 130, 140, 150, 150, 160, 170, 180, 210, 220, 230, 240, 250, 260, 280, 280, 290, 290, 290, 310, 320, 320, 370, 380, 390, 410, 440, 450, 470, 510, 530, 620, 810}

(**a**)

An outlier of a data set is a value that is very different from the other values of a data set. It is either too large or too small.

The most common way to determine whether a data set consists of any outliers of not is,

- Data value that less than <em>Q</em>₁ - 1.5 <em>IQR</em> are outliers.
- Data values that are more than <em>Q</em>₃ + 1.5 <em>IQR</em> are outliers.

Here

<em>Q</em>₁ = first quartile

<em>Q</em>₃ = third quartile

<em>IQR</em> = Inter-quartile range = <em>Q</em>₃ - <em>Q</em>₁.

The first quartile is the value that is more than 25% of the data values. The first quartile is the median of the first half of the data.

Compute the value of first quartile as follows:

First half of data: {120, 130, 130, 140, 150, 150, 160, 170, 180, 210, 220, 230, 240, 250, 260, 280, 280}

There are 17 values.

The median of an odd data set is the middle value.

The middle value is: 180

The first quartile is **<em>Q</em>****₁ = 180**.

The third quartile is the value that is more than 75% of the data values.

Compute the value of first quartile as follows:

Second half of data: {290, 290, 290, 310, 320, 320, 370, 380, 390, 410, 440, 450, 470, 510, 530, 620, 810}

There are 17 values.

The median of an odd data set is the middle value.

The middle value is: 390

The third quartile is **<em>Q</em>****₃ = 390**.

Compute the inter-quartile range as follows:

<em>IQR</em> = <em>Q</em>₃ - <em>Q</em>₁

= 390 - 180

= 210

Compute the value of [<em>Q</em>₁ - 1.5 <em>IQR</em>] as follows:

Compute the value of [<em>Q</em>₃ + 1.5 <em>IQR</em>] as follows:

There are no values that are less than [<em>Q</em>₁ - 1.5 <em>IQR</em>]. But there is one value that is more than [<em>Q</em>₃ + 1.5 <em>IQR</em>].

<em>X</em> = 810 > [<em>Q</em>₃ + 1.5 <em>IQR</em>] = 705

Thus, the outlier in the data is **$810**.

(**b**)

A distribution is known as to be skewed to the right, or positively skewed, when maximum of the data are collected on the left of the distribution.

In the stem plot above, it is shown that maximum of the data values are collected on the left of the chart. This implies that the distribution is positively skewed.

Thus, the distribution of money spent on textbooks for the 34 students is **right skewed**.