Question

1. Find the 75^th percentile of the following data (3 points): 100, 117, 95, 108, 124, 80, 93, 107

2)         A researcher wanted to study the coffee drinking habits of women ages 25 to 40. She took a sample of 6 women and asked them how many ounces of coffee they had that day. She got the following responses: 12, 8, 14, 12, 0, 20

1. What is the population she is working with? (1 point)

What is the sample mean, median and mode for number of ounces of coffee? (4 points)   

What is the sample variance and sample standard deviation for the data? (4 points)

Answer 1

(first part) find the 75th percentile of the following data (3 points): 100, 117, 95, 108, 124, 80, 93, 107 ?

after arranging in ascending order 80,93,95,100,107,108,117,124,

there are 8 observations and 75th percentile will be next to 8*75/100=6th observations, i.e. 117

(second part)

the population she is working with: coffee drinking habits of women ages 25 to 40.

What is the sample mean, median and mode for number of ounces of coffee? (4 points)

sample mean=(12+8+14+12+0+20)/6=11

sample median=middle observations=(average of 3rd and 4th observations)=(12+12)/2=12

mode=12(most-common or most-frequently occurring value in a series of data)

What is the sample variance and sample standard deviation for the data? (4 points)

sample variance=sum(x-mean)²/(n-1)=222/(6-1)=44.4

sample standard deviation=sqrt(sample variance)=sqrt(44.4)=6.66

sn	x	x-mean	(x-mean)2
1	0	-11	121
2	8	-3	9
3	12	1	1
4	12	1	1
5	14	3	9
6	20	9	81
sum=	66	0	222