Question

1. A random sample of BMI from college students were collected as follows:

23 32 34 26 23 28 38 33 25 29 28

1. Find sample size.
2. Find sample median.
3. Find sample mean.
4. Find IQR.
5. Construct a box plot.
6. Mention one reason that box plot is useful
7. What aspect of the data are both the sample standard deviation and IQR measuring? List an advantage and disadvantage of each.
8. If each person’s BMI in the sample increase the same amount, 5, how the median and IQR will change?

Answer 1

a.

Sample size = 11

b.

c.

d.

We use Excel function "Quartile()" to find the quartiles

Q₃ = 32.5

Q₁ = 25.5

IQR = Q₃ - Q₁ = 32.5 - 25.5 = 7

e.

f.

A box plot is a highly visually effective way of viewing a clear summary of one or more sets of data. It is particularly useful for quickly summarizing and comparing different sets of results from different experiments. At a glance, a box plot allows a graphical display of the distribution of results and provides indications of symmetry within the data.

g.

Both the sample standard deviation and IQR are Measures of Dispersion

The measure of dispersion indicates the scattering of data. It explains the disparity of data from one another delivering a precise view of the distribution of data. The measure of dispersion displays and gives us an idea about the variation and central value of an individual item.

For standard deviation :

Advantage : Standard deviation is least affected by the sampling fluctuations than other measures

Disadvantage : Standard deviation is highly affected by the extreme values in the series.

For IQR :

Advantage : It is not affected by extreme values

Disadvantage : It is most reliable only with symmetrical data series

h.

Median will increase by the value of 5

IQR will not change at all