Frequency Distribution Example
Practice Problem
The following data are the average monthly after-tax salary (in dollars) in 2020 for 162 countries.
6301.73 2693.05 1250 713.11 502.19 350 4479.8 2650.03 1226.79 712.5 500 350 4330.98 2564.89 1081.73 710.22 492.13 346.48 4323.25 2495.86 1080.44 701.28 491.37 340.22 4250 2495.43 1020.48 686.16 487.08 334.6 4215.43 2470.36 1018.58 667.58 481.21 330.73 4038.08 2457.33 1017.82 650 474.66 312.89 3990.69 2236.71 979.6 644.09 466.74 304.25 3780.69 2228.21 953.44 636.99 464.89 299.37 3313.01 2176.15 949.5 633.02 460 281.62 3269.62 2174.36 947.95 632.67 452.11 281.33 3258.85 2117.76 937.16 627.3 447.61 274.1 3200 2087.14 914.97 614.24 434.19 267.21 3181.11 1911.78 905.62 592.5 425.61 264.33 3081.34 1874.63 869.71 589.82 421.11 251.75 3025 1786.07 862.6 572.85 415.59 249 2991.21 1704.12 808.02 570.79 400 244.09 2960.54 1703.52 786.93 564.76 393.03 243.94 2937.58 1635.15 779.04 564.23 386.85 239.31 2924.1 1625 770.21 562.45 379.79 229 2851.85 1618.85 757.92 533.33 365 213.58 2833.33 1562.2 757.22 528.84 360.72 209.33 2782.43 1441 756.06 524.84 359.29 200 2773.5 1400.01 731.68 522.86 357.71 191.18 2761.99 1337.74 731.14 507.08 352.62 166.49 2759.38 1307.43 729.94 506.76 351.83 39.37 2731.12 1275.66 719.49 502.78 351.22 25.05
(a) Construct a frequency distribution for these data using five class intervals.
(b) Construct a frequency distribution for the data using 10 class intervals.
© Examine the results of (a) and (b) and comment on the usefulness of the frequency distributions
in summarizing these data.
Solution
We need a range to calculate bins. To calculate range we need min and max values of data
Min Value = min(data) = 25.05
Max Value = max(data) = 6301.73
Range = Max Value — Min Value = 6301.73–25.05 = 6276.68
(a) Construct a frequency distribution for these data using five class intervals.
5 bins interval value = 6276.68 / 5 = 1255.336 ~= 1255
Frequency Table:
(b) Construct a frequency distribution for the data using 10 class intervals.
10 bins interval value = 6276.68 / 10 = 627.668 ~= 628
Frequency Table
© Examine the results of (a) and (b) and comment on the usefulness of the frequency distributions
25 to 1280 data bin has almost 67% of data
when it has been split into half 25 to 653 bin has taken more data. (10 interval data table)
So, if business has to target something, then business has to give first priority to 25 to 653 bin.
More data bins are always good, but optimal number of bins should be there. If the bins are too many then it’s almost ,clumsy and it may be almost equal to data too sometimes.🤣😂😂
Note: The notation (25, 653] indicates that the lower end is not included in this interval, but the upper end is included.
