Question

1. The table provides the number of facebook friends for a sample of people aged 18 – 25.

a) Determine the percentiles far each of the number of friends intervals.

b) Determine the quartiles and the interquartile range.

c) Make box and whisker plot.

d) Determine whether there are any outliers.

Frequency 3 18 16 35 Number of Friends 0-25 25-50 50-75 75-100 100-125 125-150 150-175 175-200 200-225 225-250 62 23 14 0 5 Non

Answer 1

we assuming in given table lower limit is exclusive.

a) the question is not clear to me. so I am assuming you are asking this :

Number of friend f cf percentile 0-25 3 3 1.69 25-50 18 21 11.80 50-75 16 37 20.79 75-100 35 72 40.45 100-125 62 134 75.28 125-150 23 157 88.20 150-175 14 171 96.07 O 175-200 171 96.07 200-225 5 176 98.88 225-250 2 178 100.00

$Q_3 = l+\frac{(\frac{3*N}{4}-m)}{f} *c= 100+\frac{\frac{3*178}{4}-72}{62}*25=124.8$$Q_1 = l+\frac{(\frac{N}{4}-m)}{f} *c = 75+\frac{(\frac{178}{4}-37)}{35} *25=80.35$

Q2 =1+ 34 - m) 1978 – 72 *C= 100+ * 25 = 106.9 62 f

IQR = Q3-Q1 = 44.44

lower range = 0

upper range = 250

16.67. 175 Qpz 8035 Q = 106.9. Az = 124.8.

To check whisker we check if any number is outside range of (Q1-IQR*1.5, Q3+IQR*1.5) = (13.7,191.5). By assuming in interval frquency is uniformly distributed. then we can expect 8 outlier, 1 on left and 7 on right.