Thirty-four college students were asked how much money they spent on textbooks for the current semester. Their responses are sho

Question

3 months ago

9

Thirty-four college students were asked how much money they spent on textbooks for the current semester. Their responses are sho

wn in the following stemplot.
1 2 3 3 4 5 5 6 7 8
2 1 2 3 4 5 6 8 8 9 9 9
3 1 2 2 7 8 9
4 1 4 5 7
5 1 3
6 2
7
8 1

Key: 1|2 = $120

a. Describe a procedure for identifying potential outliers, and use the procedure to decide whether there are outliers among the responses for the money spent on textbooks.
b. Based on the stemplot, write a few sentences describing the distribution of money spent on textbooks for the 34 students.

Mathematics

1 answer:

lawyer [12.5K] · Answer 1 · 2026-02-15T23:43:42+03:00

Answer:

(a) The data point that is considered an outlier is $810.

(b) The distribution regarding expenditures on textbooks among the 34 students is right skewed.

Step-by-step explanation:

The provided data regarding how much 34 college students spent on textbooks 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 is defined as a value significantly different from the rest of the dataset, being either excessively high or low.

A widely-used approach for identifying outliers involves:

Identifying values that fall below Q₁ - 1.5 IQR as outliers.
Identifying values that exceed Q₃ + 1.5 IQR as outliers.

In our case,

Q₁ = first quartile

Q₃ = third quartile

IQR = Interquartile range = Q₃ - Q₁.

The first quartile value corresponds to more than 25% of the data points. It can be found by examining the median of the first half of the data.

Calculate the first quartile with the set below:

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

This subset contains 17 values.

The median in an odd-sized dataset is the central point.

The central value here is: 180

Thus, the first quartile is Q₁ = 180.

The third quartile value corresponds to more than 75% of the data points.

We determine the third quartile from the second half of the data:

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

The median of an odd dataset serves as the middle value.

The central point is: 390

Hence, the third quartile is Q₃ = 390.

Calculate the interquartile range as follows:

IQR = Q₃ - Q₁

= 390 - 180

= 210

Next, we compute the value of [Q₁ - 1.5 IQR]:

$Q_{1}-1.5\ IQR =180-(1.5\times 210)=-135$

And then we compute [Q₃ + 1.5 IQR]:

$Q_{3}+1.5\ IQR =390+(1.5\times 210)=705$

There are no values below [Q₁ - 1.5 IQR]. However, one value exceeds [Q₃ + 1.5 IQR].

X = 810 > [Q₃ + 1.5 IQR] = 705

Consequently, the outlier identified within the dataset is $810.

(b)

A distribution is classified as positively skewed or right-skewed when the majority of the data congregates on the lower end of the spectrum.

The stem plot indicates that most of the data values are concentrated on the left side, confirming that the distribution is indeed right skewed.

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