Quartile statistics

Use the following data, which was obtained from a study of weights of adult men, to answer problems:

Mean	192 lb	First quartile	178lb
Median	185lb	Third quartile	232 lb
Mode	180 lb	86th percentile	239 lb
Standard Deviation	23lb

a) What is the most common weight?
b) What weight did half of those surveyed exceed?
c) About what percent of those surveyed weighed more than 232lb?
d) About what percent of those surveyed weighed less than 178 lb?
e) About what percent of those surveyed weighed more than 239lb?
f) If 100 men were surveyed, what is the total weight of all the men?
g) What weight represent two standard deviations above the mean?
h) What weight represents 1.8 standard deviations below the mean?

Correct answer:

a =  180 lb
b =  185 lb
c =  25 %
d =  25 %
e =  14 %
f =  19200 lb
g =  238 lb
h =  150.6 lb

Step-by-step explanation:

$$\begin{gathered} \mu =192\text{lb} \\ \sigma =23\text{lb} \\ a=mode \\ a=180=180\text{lb} \end{gathered}$$

$$\begin{gathered} b=Median \\ b=185=185\text{lb} \end{gathered}$$

$$\begin{gathered} x>Q_3 \\ c=100-75=25\% \end{gathered}$$

$$\begin{gathered} x<Q_1 \\ d=25=25\% \end{gathered}$$

$$\begin{gathered} x>p_{86} \\ e=100-86=14\% \end{gathered}$$

$f=100\cdot \mu =100\cdot 192=19200\text{lb}$

$g=\mu +2\cdot \sigma =192+2\cdot 23=238\text{lb}$

$h=\mu -1.8\cdot \sigma =192-1.8\cdot 23=150.6\text{lb}$

Try another example