Question

The Motel Owner Association conducted a survey regarding weekday motel rates in the area. Listed below is the room rate for business-class guests for a sample of 10 motels.

$ 101, $96, $103, $110, $78, $87, $101, $80, $106, and $88.

1. Compute the mean of the above data.
2. Compute the inter quartile range.
3. Compute the standard deviation.
4. Find the mode.

Answer 1

a. The mean of the observations are: (101+ 96+ 103+ 110+ 78+ 87+ 101+ 80+ 106+ 88)/10 = 950/10 = 95.

b. We arrange the dataset from smallest to largest:

78, 80, 87, 88, 96, 101, 101, 103, 106, 110.. The interquartile range is the difference of 1st quartile and the 3rd quartile. In thisdata set, the median lies between the 5th and 6th values, i.e. 96 and 101. So, we are dividing the dataset into two parts. Now, in the left part, the 5 observations have its median in the 3rd observation, which is 87. It is the 1st quartile. In the right part, similarly, 3rd observation of that portion, which is the 7th observation of the whole dataset, is the 3rd quartile. They are 87 and 103 respectively. So, the interquartile range is: 103-87=16.

c. The variance will be: (sum(xi-x_bar)^2)/10 = (sum(xi-95)^2)/10 = 1110/10 = 111

So, standard deviation= 111^0.5= 10.5356

d. in the dataset, 101 has frequency 2, greater than other observations' frequencies. So, the mode is 101.