Question

the data set represents the number of errors on a typing test. 5 6 8 8 9 9 10 10 10 12 a. what is the median? interpret this value in the situation. b. what is the iqr?

Explanation:

Step1: Arrange data in order

The data set 5, 6, 8, 8, 9, 9, 10, 10, 10, 12 is already in ascending - order.

Step2: Find the median

There are \(n = 10\) data points. The median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered values. \(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\). The 5th value is 9 and the 6th value is 9. Median\(=\frac{9 + 9}{2}=9\). Interpretation: Half of the people taking the typing test made 9 or fewer errors, and half made 9 or more errors.

Step3: Find the lower and upper quartiles

The lower half of the data is 5, 6, 8, 8, 9. The median of the lower half (\(Q_1\)) is 8. The upper half of the data is 10, 10, 10, 12. The median of the upper half (\(Q_3\)) is 10.

Step4: Calculate the IQR

The inter - quartile range \(IQR=Q_3 - Q_1\). So, \(IQR = 10-8 = 2\).

Answer:

a. Median: 9. Half of the people taking the typing test made 9 or fewer errors, and half made 9 or more errors.
b. IQR: 2