Stat question

Question

The time (in minutes) it takes to read Chapter 2 of a statistics textbook is recorded for 11 students: 32 25 37 29 54 21 29 30 35 18 47 a. Make a stem-and-leaf display of these data. b. Compute the mean, median and mode. c. Compute the sample variance and standard deviation. d. Make a box-and-whisker plot and find the interquartile range.

Answer 1

Stem-and-leaf displays is a bit of non-specific topic...

 

For part b. we can find mean, median, and mode numerically,

 

First lets put the data points we are given in increasing order:

 

18, 21, 25, 29, 29, 30, 32, 35, 37, 47, 54

 

Mean or Average is given by the sum of data divided by number of data points...so add these 11 numbers up and divide by 11 to find the mean!

 

Median is given by the middle point (or average of the 2 middles when we have an even number of data points) when they are listed from smallest to largest (or largest to smallest)....in this case we seek the 6th or middle element of the list above....you can see that the median is 30, since there are 5 reading-times which are smaller and 5 reading-times that are larger than 30 in our list of data points.

 

The mode is the most commonly repeated data point.  For this data set the only repeated time is 29minutes, so that is the mode of this data set.

 

c.  To compute variance we sum the square differences of each point with the average or mean.  From part b1) we have found the mean as the SUM/11, lets call this \mu...for each point in our data set x_i (for i=1 to 11), we consider

(x_i - \mu)^2 and average them to find the VARIANCE...i.e. VARIANCE = 1/11 * SUM_{i=1...11} (x_i - \mu)^2

 

The standard deviation is then given by the square root of the variance.

 

d.  Making a box and whisker plot is something that EXCEL does very well.