Question

Descriptive Statistics questions MathA100 (Liberal Arts Mathematics)

Gather a sample to analyse, describe how your sample was gathered.

Ask as many people as you can (or at least 30) the following two questions:

"what is the brand of the car you drive?" (Toyota, KIA, Jeep, etc)

"what is the model year of that car?"

1. Construct a bar graph and a pie chart of the brand names

2. Find the mean, median, and standard deviation of the model year

3. Construct a histogram of the model year, decide if it looks approximately normal or not

4. Construct a box plot of the model year, check your data for any outlier

Answer 1

This is a randomly generated data. While Collecting actual data you have to pick people randomly to avoid any bias.

a) percentage is find by frequency divide by total.

2 Mean calculated as:

.

Varinace is computed as:

Since it is a sample:

where:

Standard deviation is calculated as:

c)

From the chart we can see that data looks approximately normal. Hence it follows normal distribution.

d) median = (n+1)/2 th = 15.5th observation the answer is 2006

quantile 1 = (n+1)/4 = 7.75th observation which is 2005

quantile 2 = 3(n+1)/4 = 23.25th obs which is 2008.

minimum value is 2000

maximum value is 2013

IQR = Q3- Q1 = 2008-2005 = 3

lower fence = quantitle 1 - 1.5*IQR = 2005-4.5 = 2000.5

upper fence = quantile3 + 1.5*IQR = 2008+4.5 = 2012.5

thus 2000 and 2013 are outlier