Question

find the following measures for the data below: 11 10 16 1 1 15 3 13 4 17 3 8 15 11 7 sorted data (use commas to separate values) quartile 1 median quartile 3 interquartile range

Explanation:

Step1: Sort the data

1, 1, 3, 3, 4, 7, 8, 10, 11, 11, 13, 15, 15, 16, 17

Step2: Find the number of data points

$n = 15$

Step3: Calculate the median position

Since $n = 15$ (odd), the median position is $\frac{n + 1}{2}=\frac{15+ 1}{2}=8$. So the median is 10.

Step4: Find the lower half of data

The lower - half data is 1, 1, 3, 3, 4, 7, 8. The number of data points in the lower - half $n_1=7$. The position of the first quartile is $\frac{n_1 + 1}{2}=\frac{7+1}{2}=4$. So $Q_1 = 3$.

Step5: Find the upper half of data

The upper - half data is 11, 11, 13, 15, 15, 16, 17. The number of data points in the upper - half $n_2 = 7$. The position of the third quartile is $\frac{n_2+1}{2}=\frac{7 + 1}{2}=4$. So $Q_3=15$.

Step6: Calculate the inter - quartile range

$IQR=Q_3 - Q_1=15 - 3=12$

Answer:

Sorted Data: 1, 1, 3, 3, 4, 7, 8, 10, 11, 11, 13, 15, 15, 16, 17
Quartile 1: 3
Median: 10
Quartile 3: 15
Interquartile Range: 12