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…

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