The following stem and leaf is constructed from the data One

The following stem- and leaf is constructed from the data. One may define an outlier in data as any observation fall beyond the limits, Lower limit: Q1 1.5 × (IQR) and Upper limit: Q3 + 1.5 × (IQR), where IQR is the interquartile range. Are there suspected outliers?

(do not round answers)

(a) Compute the five-number summaries from data given in stem and leaf plot.

Min:

Max:

Q1:

Q2:

Q3:

(b) Find the range (R).

(c) Estimate the estimated standard deviation (s) of the data using R.

(d) Compute the interquartile range.

(e) List any suspected outliers, and bounds from IQR rule.

(type outliers separated by a single space only).

Lower Bound:

Upper Bound:

Outliers:

Solution

five number summary

minimum    1

q1               3

median         10

q3               15

maximum      39

the range is equal to highest - lowest

therefore range = 39-1 = 38

c) Population size:7
Mean (): 11.857142857143

Standard deviation (): 12.099924101634

d) subtract the 75th percentile from the 25th percentile to find the interquartile range using the formula Q₃ – Q₁ =IQR. from above q3-q1 = 15-3=12