Question 1 Actual lengths of stay at a hospital\'s emergency department in 2009

ID: 3063817 • Letter: Q

Question

Question 1 Actual lengths of stay at a hospital's emergency department in 2009 are shown in the following table (rounded to the nearest hour). Length of stay is the total of wait and service times. Some longer stays are also approximated as 15 hours in this table. Hours Count Percent 10 2.08 2 41 8.54 3 87 18.13 4 107 22.29 5 83 17.29 6 63 13.13 7 36 7.50 8 13 2.71 9 15 3.13 10 14 2.92 15 11 2.29 Calculate the mean and variance for the random variable (length of stay). Round your answers to two decimal places (e.g. 98.76) Mean- Variance-

Explanation / Answer

Hours(x)

Count(f)

x * f

x^2 * f

1 * 10 = 10

1^2 * 10 = 10

2 * 41 = 82

2^2 * 41 = 164

3 * 87 = 261

3^2 * 87 = 783

107

4 * 107 = 428

4^2 * 107 = 1712

5 * 83 = 415

5^2 * 83 = 2075

6 * 63 = 378

6^2 * 63 = 2268

7 * 36 = 252

7^2 * 36 = 1764

8 * 13 = 104

8^2 * 13 = 832

9 * 15 = 135

9^2 * 15 = 1215

10 * 14 = 140

10^2 * 14 = 1400

15 * 11 = 165

15^2 * 11 = 2475

sum(f) = 480

sum(x * f) = 2370

sum(x^2 * f) = 14698

mean (x)= sum(x * f)/sum(f)= 2370/480= 4.94

variance(x) = sum(x^2 *f)/sum(f) - mean^2 = 14698/480 – 4.94^2= 6.24