Question

The following data were collected as part of a study of coffee consumption among medical students. The following reflect cups per day consumed:

3          4          6          8          2          1          0          2

First, put the data in order from lowest to highest:

0, 1, 2, 2, 3, 4, 6, 8

This will help you to find the median and the quartiles!

1) Compute the sample mean and round to one decimal place (see page 100). ____

2) Compute the sample median and round to one decimal place (see page 88). _____

3) Compute the sample standard deviation and round to one decimal place. I have computed the sample variance for you = 7.36 (see page 110). ______

(see page 88-91 for quartiles and outliers)

The interquartile range (IQR) is a number that indicates the spread of the middle half or the middle 50% of the data. It is the difference between the third quartile (Q₃) and the first quartile (Q₁). IQR = Q₃ – Q₁

The IQR can help to determine potential outliers. A value is suspected to be a potential outlier if it is less than (1.5)(IQR) below the first quartile or more than (1.5)(IQR) above the third quartile. Potential outliers always require further investigation.

4) Compute the first quartile and round to one decimal place. ______

5) Compute the third quartile and round to one decimal place. _____

6) Compute the interquartile range and round to one decimal place. _____

Checking for outliers requires two answers, both #7 & 8):

7) Using the interquartile range, calculate for outliers and round to two decimal places. _______

8) Using the interquartile range, calculate for outliers and round to two decimal places. _______

9) Are there any outliers? Yes or no? ______

Answer 1

1 Sample mean (n)=8 = 26 = 3.25 =3+3 2) Sample median ) = 2+3 = 2.5 3 Sample varian ca 8 h ($22 - (22) = (134 s? 7.0714 ) Sample Standard deviation - 532=57014 a 20659 a 6 © G = 2.7 first Quartile (Q)= ht= 9=2025 place=1.25 =(1-3) Rird Quartice (0) = 3 (nt) = 3x - 675 pale 24 fon5x2) = 15.5 I QR = Q-Q1 = 5.5-1.3 =142 Lower inner fence = 0, -0.5XIOR) = 1.3-(1.5x4.2) ® upper innertence art (115x IQR)=55+(115x402) 118 no out liers, No There are