Select the outlier in the data set. 20, 27, 33, 39, 51, 60, 76, 94, 685

Arrange Data Set: Arrange the data set in ascending order. The data set is already in ascending order: 20, 27, 33, 39, 51, 60, 76, 94, 685.Calculate IQR: Calculate the interquartile range (IQR) of the data set. First, find the median (Q2), which is the middle value when the data is ordered. For our data set, the median is 51. Next, find Q1, the median of the lower half of the data set (not including Q2). The lower half is 20, 27, 33, 39, so Q1 is the average of 27 and 33, which is (27 + 33) / 2 = 30. Then, find Q3, the median of the upper half of the data set (not including Q2). The upper half is 60, 76, 94, 685, so Q3 is the average of 76 and 94, which is (76 + 94) / 2 = 85. Now, calculate the IQR: IQR = Q3 - Q1 = 85 - 30 = 55.Determine Outlier Boundaries: Determine the outlier boundaries. The lower boundary for outliers is Q1 - 1.5 * IQR = 30 - 1.5 * 55 = 30 - 82.5 = -52.5 (since there can't be negative values in this context, we'll consider the lower boundary as the smallest value in the data set, which is 20). The upper boundary for outliers is Q3 + 1.5 * IQR = 85 + 1.5 * 55 = 85 + 82.5 = 167.5.Identify Outliers: Identify any values outside the outlier boundaries. Looking at the data set, the value 685 is clearly above the upper boundary of 167.5, so it is an outlier.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Select the outlier in the data set. $\newline$ $20, 27, 33, 39, 51, 60, 76, 94, 685$

View step-by-step help

Home

Math Problems

Grade 6

Calculate quartiles and interquartile range

Full solution

Q. Select the outlier in the data set.

\newline

20, 27, 33, 39, 51, 60, 76, 94, 685

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $20, 27, 33, 39, 51, 60, 76, 94, 685$ .
Calculate IQR: Calculate the interquartile range (IQR) of the data set. $\newline$ First, find the median $Q_2$ , which is the middle value when the data is ordered. For our data set, the median is $51$ . $\newline$ Next, find $Q_1$ , the median of the lower half of the data set (not including $Q_2$ ). The lower half is $20, 27, 33, 39$ , so $Q_1$ is the average of $27$ and $33$ , which is $\frac{27 + 33}{2} = 30$ . $\newline$ Then, find $Q_3$ , the median of the upper half of the data set (not including $Q_2$ ). The upper half is $51$ $1$ , so $Q_3$ is the average of $51$ $3$ and $51$ $4$ , which is $51$ $5$ . $\newline$ Now, calculate the IQR: $51$ $6$ .
Determine Outlier Boundaries: Determine the outlier boundaries. $\newline$ The lower boundary for outliers is $Q1 - 1.5 \times IQR = 30 - 1.5 \times 55 = 30 - 82.5 = -52.5$ (since there can't be negative values in this context, we'll consider the lower boundary as the smallest value in the data set, which is $20$ ). $\newline$ The upper boundary for outliers is $Q3 + 1.5 \times IQR = 85 + 1.5 \times 55 = 85 + 82.5 = 167.5$ .
Identify Outliers: Identify any values outside the outlier boundaries. $\newline$ Looking at the data set, the value $685$ is clearly above the upper boundary of $167.5$ , so it is an outlier.