Questions: Find the median for the group of data items. 99, 99, 91, 35, 73, 99 A. 95 B. 35 C. 99 D. 91

Solution Steps

To find the median, we first sort the data set. The given data items are: \[ 99, 99, 91, 35, 73, 99 \] After sorting, we have: \[ \text{Sorted data} = [35, 73, 91, 99, 99, 99] \]

The formula for the rank \( R \) to find the median (quantile \( Q \)) is given by: \[ R = Q \times (N + 1) \] where \( N \) is the number of data points. Here, \( N = 6 \) and \( Q = 0.5 \) (for the median). Thus, we calculate: \[ R = 0.5 \times (6 + 1) = 0.5 \times 7 = 3.5 \]

Since \( R = 3.5 \) is not an integer, we take the average of the values at ranks 3 and 4 in the sorted data. The values at these ranks are:

• \( X_{\text{lower}} = 91 \) (rank 3)
• \( X_{\text{upper}} = 99 \) (rank 4)

Using the averaging formula: \[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{91 + 99}{2} = \frac{190}{2} = 95.0 \]

Final Answer