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Josh is on the basketball team and scored the following number of points per game for the last 10 games: \( 6,7,8,8,10,10,11,14,15,26 \) Minimum: Q1: Qedian: Maximum: IQR: Check for outliers... Low End: High End: The outlier is there is no outlier,

Ask by Bates Wyatt. in the United States
Mar 09,2025

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**Minimum:** 6 **Q1:** 8 **Median:** 10 **Maximum:** 26 **IQR:** 6 **Outlier:** 26

Solución

**Minimum:** \(6\) **Q1:** Sort the lower half of the data (first 5 values for 10 data points): \(6,\,7,\,8,\,8,\,10\) The median of these values is the third value: \(8\) **Median:** For 10 data points, the median is the average of the 5th and 6th values in the sorted list. The 5th value is \(10\) and the 6th value is \(10\). \[ \text{Median} = \frac{10 + 10}{2} = 10 \] **Maximum:** \(26\) **IQR:** First, find Q3, the median of the upper half (last 5 values): Upper half: \(10,\,11,\,14,\,15,\,26\) The median here is the third value: \(14\) Now compute the IQR: \[ \text{IQR} = Q3 - Q1 = 14 - 8 = 6 \] **Check for Outliers:** Calculate the low and high end cutoffs using \(1.5 \times \text{IQR}\). \[ \text{Low End} = Q1 - 1.5 \times \text{IQR} = 8 - 1.5 \times 6 = 8 - 9 = -1 \] \[ \text{High End} = Q3 + 1.5 \times \text{IQR} = 14 + 9 = 23 \] Any data value below \(-1\) or above \(23\) is an outlier. In the dataset, \(26\) is above \(23\). **Outlier:** \(26\) is an outlier.

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To break down Josh's basketball scoring, let's first calculate the essential statistics. The minimum score is 6, and the maximum is an impressive 26. To find the first quartile (Q1), we take the average of the second and third scores in the ordered set (7 and 8), which gives us Q1 = 7.5. For the median (Q2), the middle score in this sorted list (10 and 11) averages to 10.5. The third quartile (Q3) takes the average of the eighth and ninth scores (14 and 15), yielding Q3 = 14.5. Now, for the IQR (Interquartile Range), subtract Q1 from Q3: IQR = Q3 - Q1 = 14.5 - 7.5 = 7. To check for outliers, we calculate the low end as Q1 - 1.5 * IQR = 7.5 - (1.5 * 7) = -0.5, and the high end as Q3 + 1.5 * IQR = 14.5 + (1.5 * 7) = 22. Since there are no scores below -0.5 and no scores above 22, the conclusion is that 26 is indeed an outlier! With all these stats in hand, Josh can now leverage his performance data to set scoring goals for improvement, ensuring he keeps climbing those points! Enjoying such insights not only enhances your game strategy but also keeps motivation levels high when aiming to break personal records!

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