Statistics homework help. Mean, Median, and Mode
Find the mean, median, mode, range, interquartile range, and standard deviation of the following two examples.
Example 1
| X (income) | No. of persons |
| 200 | 24 |
| 250 | 26 |
| 180 | 16 |
| 300 | 20 |
| 350 | 6 |
| 280 | 30 |
Solution
| X (income) | No. of persons | Fx | CF | (x-m)^2 | (x-m)^2*f |
| 180 | 16 | 2880 | 16 | 5108.73 | 81739.75 |
| 200 | 24 | 4800 | 40 | 2649.72 | 63593.23 |
| 250 | 26 | 6500 | 66 | 2.18 | 56.60 |
| 280 | 30 | 8400 | 96 | 813.65 | 24409.57 |
| 300 | 20 | 6000 | 116 | 2354.64 | 47092.72 |
| 350 | 6 | 2100 | 122 | 9707.09 | 58242.57 |
| Total | 122 | 30680 | 20636.01 | 275134.43 |
Mean: 251.47
Median: 250
Mode: 280
Range: 170
Interquartile Range: 30
Standard Deviation: 47.49
Example 2
| X (income) | No. of persons | Cumulative frequency (cf) |
| 180 | 16 | 16 |
| 200 | 24 | 40 |
| 250 | 26 | 66 |
| 280 | 30 | 96 |
Solution
| X (income) | No. of persons | Cumulative frequency (cf) | xf | (x-m)^2 | (x-m)^2*f |
| 180 | 16 | 16 | 2880 | 3047.96 | 48767.36 |
| 200 | 24 | 40 | 4800 | 1239.63 | 29751.04 |
| 250 | 26 | 66 | 6500 | 218.79 | 5688.63 |
| 280 | 30 | 96 | 8400 | 2006.29 | 60188.80 |
| Total | 96 | 218 | 22580 | 6512.67 | 144395.83 |
Mean: 235.21
Median: 250
Mode: 280
Range: 100
Interquartile Range: 100
Standard Deviation: 38.78
