In: Statistics and Probability
Make an ungrouped frequency distribution for Price/Sales. Use the frequency distribution to find the mean, median, mode and standard deviation for Price/Sales ratio. (Note the boldface – must show and describe steps for how you USED the frequency distribution to compute the statistics)
Price to Sales |
(ratio) |
0.8 |
0.4 |
0.2 |
1.1 |
1.2 |
0.4 |
0.4 |
0.1 |
0.3 |
0.6 |
0.3 |
0.2 |
0.1 |
0.2 |
0.7 |
0.2 |
0.2 |
0.7 |
0.1 |
0.3 |
0.7 |
0.6 |
0.1 |
0.1 |
0.3 |
0.5 |
0.5 |
0.5 |
0.4 |
0.8 |
0.6 |
0.2 |
0.5 |
0.1 |
0.1 |
0.1 |
1.2 |
0.6 |
0.2 |
0.5 |
0.9 |
0.5 |
0.5 |
(a) we have a total of 43 data values, so n = 43
mean = (sum of all data values)(total number of data values)
So, mean = 0.44186 or 0.4 (rounded to 1 decimal place)
(b) Total number of data value is 43, i.e. odd number of data values
Median for odd data values is the middle or center data value. In this case, median will be the 22nd data value
First arrange data in ascending order, then select the 22nd data value
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.1 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.2 |
0.3 |
0.3 |
0.3 |
0.3 |
0.4 |
0.4 |
0.4 |
0.4 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
0.5 |
0.6 |
0.6 |
0.6 |
0.6 |
0.7 |
0.7 |
0.7 |
0.8 |
0.8 |
0.9 |
1.1 |
1.2 |
1.2 |
So, median = 0.40
(c) Formula for standard deviation is
where xi are given data values and x(bar) = mean = 0.4 and n = 43
setting the values, we get
(rounded to 2 decimals)