Answer to Question #278974 in Statistics and Probability for Kelvin

Question

The recovery time in days for 36 patients are given below

8 7 6 4 5 3 7 8 10 7 7

6 4 10 3 6 8 2 5 4 5 3 8

7 4 6 3 7 12 4 3 6 6 9 4

A. Construct a frequency distribution

B. What percentage of recovery days were fewer than 6

C. Find the mean and median number of days to recovery

D. Fin the 20th percentile and the samllr variance

Answer 1

Least to Greatest Value:

2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 10, 10, 12

A.

value frequency

2 1

3 5

4 6

5 3

6 6

7 6

8 4

9 1

10 2

12 1

B.

$15/35=0.4286=42.86\%$

C.

mean:

$\mu=\sum x_i/n=5.91$

median is the value separating the higher half from the lower half of a data sample

in our case, n = 35, so median is 18th value:

median = 6

D.

sample variance:

$s^2=\frac{\sum (x_i-\mu)^2}{n-1}=5.49$

$P_{20}=(20(n+1)/100)$th value of the observation

$P_{20}=(20(35+1)/100)=(7.2)$th value of the observation

= 7th observation + 0.2(8th-7th) = $4+0.2(4-4)=4$