For the following set of data, find the population standard deviation, to the nearest hundredth.
Data Frequency
13 77
14 99
28 66
29 44
30 66
32 66
39 66
4040 33
5050 22
To find the population standard deviation, we will first calculate the mean of the data set:
(13 * 77) + (14 * 99) + (28 * 66) + (29 * 44) + (30 * 66) + (32 * 66) + (39 * 66) + (40 * 33) + (50 * 22)
= 1001 + 1386 + 1848 + 1276 + 1980 + 2112 + 2574 + 1320 + 1100
= 13497
Then, we add up the frequencies:
77 + 99 + 66 + 44 + 66 + 66 + 66 + 33 + 22
= 483
Now, we can calculate the population standard deviation using the formula:
Population Standard Deviation = √(∑((X - Mean)^2 * Freq) / N)
= √((4900 + 4851 + 3084 + 7437 + 3844 + 1024 + 11236 + 16812 + 2209) / 483)
= √((70,587) / 483)
= √146.35
= 12.10
Therefore, the population standard deviation of the data set is 12.10 to the nearest hundredth.