Homework SourseI need the mean median mode range standard deviation varianc
I need the mean, median, mode, range, standard deviation, variance, and IQR for the data set below:
| $ 156,077,912.00 |
| $ 84,308,755.00 |
| $ 67,261,251.00 |
| $ 63,601,493.00 |
| $ 47,077,699.00 |
| $ 46,497,018.00 |
| $ 40,313,856.00 |
| $ 29,247,871.00 |
| $ 28,144,047.00 |
| $ 26,642,438.00 |
| $ 25,224,422.00 |
| $ 24,537,936.00 |
| $ 24,455,192.00 |
| $ 23,984,315.00 |
| $ 23,270,044.00 |
| $ 22,796,083.00 |
| $ 22,042,128.00 |
| $ 21,466,454.00 |
| $ 21,426,391.00 |
| $ 20,612,945.00 |
Solution
First arrange the data in ascending order to make the calculation easy.
Following table shows the sorted data in ascending order.
The descriptive statistics comprising of the Mean, Median, Mode, Range, Standard Deviation, and Variance can be obtained in excel from the \"Data Analysis\" add on by using the \"descriptive statistics\" option.
Following is the output -
and the IQR is defined as -
IQR = 3rd Quartile - 1st Quartile
As there are 20 observations, so the first quartile is the average of the 5th and 6th term while third quartile is the average of 15th and 16th term.
So, 1st quartile = 23033063.5
And, 3rd Quartile = 46787258.5
So, IQR = 23754295.
You can calculate the Median, range, IQR manually. But the calculation of Mean, Standard deviation and variance will be too complicated to do it manually.
| S.No. | Value |
| 1 | 20612945 |
| 2 | 21426391 |
| 3 | 21466454 |
| 4 | 22042128 |
| 5 | 22796083 |
| 6 | 23270044 |
| 7 | 23984315 |
| 8 | 24455192 |
| 9 | 24537936 |
| 10 | 25224422 |
| 11 | 26642438 |
| 12 | 28144047 |
| 13 | 29247871 |
| 14 | 40313856 |
| 15 | 46497018 |
| 16 | 47077699 |
| 17 | 63601493 |
| 18 | 67261251 |
| 19 | 84308755 |
| 20 | 156077912 |
