Question

bags of chips sold by asb per week:

1. use the dot plot to make two box plots of the data over the same number line: one plot with the outliers and one plot without the outliers
2. what is the iqr with the outliers?
3. what is the iqr without the outliers?
4. what is the range with the outliers?
5. what is the range without the outliers?
6. which is affected more by the outliers: the range or the iqr?

quiz scores:

1. make a dot plot and two box plots of the data over the same number line: one plot with the outliers and one plot without the outliers
2. what is the iqr with the outliers?
3. what is the iqr without the outliers?
4. what is the range with the outliers?
5. what is the range without the outliers?
6. which is affected more by the outliers: the range or the iqr?

Explanation:

First, extract the data from the dot plot for bags of chips:
Data set (with outliers): 14, 20, 22, 24, 24, 26, 26, 30, 32, 34, 36, 44
First, identify outliers using IQR rule:

Step1: Sort the full data set

$14, 20, 22, 24, 24, 26, 26, 30, 32, 34, 36, 44$

Step2: Find median (Q2) of full set

$n=12$, median = $\frac{26+26}{2}=26$

Step3: Find Q1 (lower half median)

Lower half: $14,20,22,24,24,26$; Q1 = $\frac{22+24}{2}=23$

Step4: Find Q3 (upper half median)

Upper half: $26,30,32,34,36,44$; Q3 = $\frac{32+34}{2}=33$

Step5: Calculate IQR with outliers

$IQR = Q3 - Q1 = 33 - 23 = 10$

Step6: Identify outliers

IQR*1.5 = $10*1.5=15$; Lower fence: $23-15=8$, Upper fence: $33+15=48$. The values 14 and 44 are within fences? No, wait, recheck: Wait, no, the outlier is values outside $Q1-1.5*IQR$ and $Q3+1.5*IQR$. 14 > 8, 44 <48, so actually no outliers? Wait no, visual outlier is 14 and 44, but by IQR rule, they are not. Wait, no, let's use visual outliers: 14 and 44 are far from the cluster. So data without outliers: $20,22,24,24,26,26,30,32,34,36$

Step7: Find Q1 for trimmed data

Trimmed data sorted: $20,22,24,24,26,26,30,32,34,36$; $n=10$, Q1 = $\frac{22+24}{2}=23$

Step8: Find Q3 for trimmed data

Q3 = $\frac{32+34}{2}=33$

Step9: IQR without outliers

$IQR = 33-23=10$

Step10: Range with outliers

$Range = Max - Min = 44-14=30$

Step11: Range without outliers

$Range = 36-20=16$

Step12: Compare range/IQR change

IQR stays 10, range changes by 14. So range is more affected.

For quiz scores: Note: No data points are provided for quiz scores, so we cannot solve questions 19-24. Please provide the dot plot data for quiz scores.

Answer:

1. 10
2. 10
3. 30
4. 16
5. The range is affected more by outliers.

19-24: Cannot be solved, as no data points (dots) are provided for the quiz scores dot plot. Please add the data points for the quiz scores number line.