Question

1. for the given frequency distribution below find the mean, median and standard deviation

X	f(X)
2	4
3	7
4	5
5	7
6	5
7	2

a) List the relative and cumulative relative frequency for each interval the table above

2. Identify the level of the following variables a. heights of male students b. the first three finisher of a car race c. temperature in fahrenheit. d. the types of cars in a parking lot

3. find the five-number summary of the following sample

(1,4,7,9,15,23,35,39,56,59,62,78)

a)Are there any outliers?

b) find the mean and median and describe its shape

c) For continuous data it is best to use a histogram or a dot plot to graphically describe its shape

d) list the relative and cumulative relative frequency for each interval

Answer 1

1:

Following table shows the calculations:

X	f(X)	xf(x)	f(x)*(x-mean)^2
2	4	8	20.557156
3	7	21	11.237023
4	5	20	0.356445
5	7	35	3.761023
6	5	30	15.016445
7	2	14	14.938578
Total	30	128	65.86667

Sample size:

Sample mean is

The sample standard deviation is :

Median: Since there are 30 data values so median will be average of 15th and 16th data values. Therefore median is

b)

Following table shows the relative frequency and cumulative relative frequency:

X	f(X), f	f/30	Cumulative relative frequency
2	4	0.1333	0.1333
3	7	0.2333	0.3666
4	5	0.1667	0.5333
5	7	0.2333	0.7666
6	5	0.1667	0.9333
7	2	0.0667	1
Total	30	1