Select the outlier in the data set. 36, 46, 54, 60, 62, 74, 88, 94, 371

Arrange Data Set: Arrange the data set in ascending order. The data set is already in ascending order: 36, 46, 54, 60, 62, 74, 88, 94, 371.Calculate Quartiles: Calculate the first quartile (Q1), the median (Q2), and the third quartile (Q3) of the data set. To find Q1, we take the median of the first half of the data set (excluding the median if there is an odd number of data points). For Q3, we take the median of the second half of the data set. First half (for Q1): 36, 46, 54, 60 Second half (for Q3): 62, 74, 88, 94 Median of first half (Q1): (46 + 54) / 2 = 50 Median of second half (Q3): (74 + 88) / 2 = 81Calculate IQR: Calculate the interquartile range (IQR). IQR = Q3 - Q1 = 81 - 50 = 31Determine Bounds: Determine the lower and upper bounds for potential outliers. Lower bound = Q1 - 1.5 * IQR = 50 - 1.5 * 31 = 50 - 46.5 = 3.5 Upper bound = Q3 + 1.5 * IQR = 81 + 1.5 * 31 = 81 + 46.5 = 127.5Identify Outliers: Identify any data points that fall outside the lower and upper bounds. The value 371 is well above the upper bound of 127.5, so it is considered an outlier.

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Select the outlier in the data set. $\newline$ $36, 46, 54, 60, 62, 74, 88, 94, 371$

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Math Problems

Grade 6

Calculate quartiles and interquartile range

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Q. Select the outlier in the data set.

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36, 46, 54, 60, 62, 74, 88, 94, 371

Arrange Data Set: Arrange the data set in ascending order. $\newline$ The data set is already in ascending order: $36, 46, 54, 60, 62, 74, 88, 94, 371$ .
Calculate Quartiles: Calculate the first quartile ( $Q_1$ ), the median ( $Q_2$ ), and the third quartile ( $Q_3$ ) of the data set. $\newline$ To find $Q_1$ , we take the median of the first half of the data set (excluding the median if there is an odd number of data points). For $Q_3$ , we take the median of the second half of the data set. $\newline$ First half (for $Q_1$ ): $36, 46, 54, 60$ $\newline$ Second half (for $Q_3$ ): $62, 74, 88, 94$ $\newline$ Median of first half ( $Q_1$ ): $Q_2$ $0$ $\newline$ Median of second half ( $Q_3$ ): $Q_2$ $2$
Calculate IQR: Calculate the interquartile range (IQR). $IQR = Q3 - Q1 = 81 - 50 = 31$
Determine Bounds: Determine the lower and upper bounds for potential outliers. $\newline$ Lower bound = $Q1 - 1.5 \times IQR = 50 - 1.5 \times 31 = 50 - 46.5 = 3.5$ $\newline$ Upper bound = $Q3 + 1.5 \times IQR = 81 + 1.5 \times 31 = 81 + 46.5 = 127.5$
Identify Outliers: Identify any data points that fall outside the lower and upper bounds. The value $371$ is well above the upper bound of $127.5$ , so it is considered an outlier.