Question

using the list of numbers below, fill in all of the blanks below! 4, 6, 6, 7, 8, 9, 10, 11, 15, 24 the mean is the mode is the median is the range is q1 is q3 is iqr is the outlier is

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{4 + 6+6+7+8+9+10+11+15+24}{10}=\frac{100}{10}=10$

Step2: Find the mode

The mode is the number that appears most frequently. Here, 6 appears twice and other numbers appear once, so the mode is 6.

Step3: Calculate the median

First, order the data: 4, 6, 6, 7, 8, 9, 10, 11, 15, 24. Since $n = 10$ (even), the median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$-th values. $\frac{8 + 9}{2}=8.5$

Step4: Calculate the range

The range is the difference between the maximum and minimum values. Range $=24 - 4=20$

Step5: Find Q1

The lower - half of the data is 4, 6, 6, 7, 8. The median of the lower - half (Q1) is 6.

Step6: Find Q3

The upper - half of the data is 9, 10, 11, 15, 24. The median of the upper - half (Q3) is 11.

Step7: Calculate the IQR

The inter - quartile range $IQR=Q3 - Q1=11 - 6 = 5$

Step8: Identify the outlier

The lower fence is $Q1-1.5\times IQR=6-1.5\times5=6 - 7.5=-1.5$
The upper fence is $Q3 + 1.5\times IQR=11+1.5\times5=11 + 7.5 = 18.5$
Since $24>18.5$, 24 is the outlier.

Answer:

The Mean is 10
The Mode is 6
The Median is 8.5
The Range is 20
Q1 is 6
Q3 is 11
IQR is 5
The Outlier is 24