Question: During July 27, 2024 to June 26, 2025, count the number of times Insulet Corporation's close price break below the 20-day Exponential Moving Average line. (Smoothing factor alpha = 2 / (n + 1); Require 4n data points to warm up; Use the first data point as the initial value) Using unadjusted prices, write down the indicator formula, collect the raw data, calculate the answer, and keep four decimal places. Please list the raw data and key calculation process.
Formula: EMA_t = \alpha * P_t + (1 - \alpha) * EMA_{t-1}, \quad \alpha = 2 / (n + 1)
Data:
date,close,high,open
2024-04-03,164.86000061035156,166.0,163.25
2024-04-04,163.25,167.27000427246094,165.72999572753906
2024-04-05,165.0,165.97000122070312,163.0500030517578
2024-04-08,170.0399932861328,170.17999267578125,166.3000030517578
2024-04-09,178.00999450683594,179.47999572753906,171.1999969482422
2024-04-10,177.41000366210938,177.63999938964844,174.0800018310547
2024-04-11,179.64999389648438,180.00999450683594,179.10000610351562
2024-04-12,175.22000122070312,178.49000549316406,177.6300048828125
2024-04-15,173.94000244140625,178.4199981689453,176.4199981689453
2024-04-16,172.7100067138672,174.82000732421875,172.8699951171875
2024-04-17,166.25999450683594,173.74000549316406,172.7100067138672
2024-04-18,164.72999572753906,169.24000549316406,166.44000244140625
2024-04-19,166.25,167.10000610351562,165.2899932861328
2024-04-22,164.4199981689453,166.75,165.72999572753906
2024-04-23,167.27000427246094,168.82000732421875,164.61000061035156
2024-04-24,167.25,169.33999633789062,168.17999267578125
2024-04-25,164.1699981689453,167.25,166.63999938964844
2024-04-26,166.19000244140625,168.42999267578125,163.32000732421875
2024-04-29,170.25999450683594,170.27000427246094,167.60000610351562
2024-04-30,171.94000244140625,174.02000427246094,168.64999389648438
2024-05-01,170.27000427246094,174.85000610351562,171.58999633789062
2024-05-02,173.4199981689453,173.60000610351562,173.02000427246094
2024-05-03,174.42999267578125,180.25,176.83999633789062
2024-05-06,176.39999389648438,177.86000061035156,175.50999450683594
2024-05-07,184.27999877929688,185.0200042724609,181.1000061035156
2024-05-08,175.57000732421875,182.9900054931641,179.0
2024-05-09,177.52999877929688,179.0399932861328,177.0
2024-05-10,165.89999389648438,193.3000030517578,181.8699951171875
2024-05-13,161.02000427246094,170.49000549316406,166.0
2024-05-14,172.27000427246094,174.30999755859375,161.80999755859375
2024-05-15,180.55999755859372,181.3000030517578,174.25
2024-05-16,185.3800048828125,185.9600067138672,180.55999755859372
2024-05-17,187.2700042724609,187.6699981689453,185.3800048828125
2024-05-20,184.13999938964844,188.97000122070312,187.2700042724609
2024-05-21,182.7899932861328,184.5,183.97999572753903
2024-05-22,181.0800018310547,184.1000061035156,182.5800018310547
2024-05-23,170.7899932861328,180.72000122070312,180.55999755859372
2024-05-24,180.07000732421875,180.22000122070312,171.41000366210938
2024-05-28,177.82000732421875,181.67999267578125,180.3300018310547
2024-05-29,172.25,177.57000732421875,175.61000061035156
2024-05-30,175.9499969482422,179.97999572753906,173.74000549316406
2024-05-31,177.19000244140625,180.6499938964844,176.85000610351562
2024-06-03,181.4199981689453,185.3000030517578,177.39999389648438
2024-06-04,181.80999755859372,184.3999938964844,181.3800048828125
2024-06-05,187.67999267578125,189.41000366210935,181.80999755859372
2024-06-06,192.4199981689453,194.5399932861328,186.6199951171875
2024-06-07,191.4199981689453,194.3800048828125,190.0
2024-06-10,192.0399932861328,192.3600006103516,189.32000732421875
2024-06-11,192.16000366210935,194.2100067138672,192.1999969482422
2024-06-12,200.6699981689453,203.69000244140625,195.0
2024-06-13,201.83999633789065,204.7400054931641,200.6999969482422
2024-06-14,200.4499969482422,202.0399932861328,201.02999877929688
2024-06-17,198.3999938964844,200.8500061035156,198.6300048828125
2024-06-18,196.3999938964844,199.0200042724609,197.58999633789065
2024-06-20,199.30999755859372,199.55999755859372,195.8999938964844
2024-06-21,204.1000061035156,204.3999938964844,200.0
2024-06-24,203.94000244140625,206.5,204.25
2024-06-25,205.75,207.72000122070312,204.05999755859372
2024-06-26,206.80999755859372,207.7700042724609,204.19000244140625
2024-06-27,206.97999572753903,208.2100067138672,207.0200042724609
2024-06-28,201.8000030517578,207.4600067138672,206.3600006103516
2024-07-01,196.16000366210935,208.8999938964844,201.8000030517578
2024-07-02,197.19000244140625,202.1999969482422,199.3300018310547
2024-07-03,196.72000122070312,199.33999633789065,198.8999938964844
2024-07-05,196.8999938964844,198.02999877929688,196.1499938964844
2024-07-08,198.6699981689453,201.0,196.2100067138672
2024-07-09,195.1699981689453,198.67999267578125,198.3600006103516
2024-07-10,197.6699981689453,197.97000122070312,195.9600067138672
2024-07-11,203.6199951171875,205.3999938964844,199.6999969482422
2024-07-12,201.97999572753903,209.3500061035156,204.0
2024-07-15,198.8699951171875,204.1300048828125,201.2700042724609
2024-07-16,201.38999938964844,205.66000366210935,200.6199951171875
2024-07-17,197.6499938964844,205.25999450683597,199.3300018310547
2024-07-18,194.9600067138672,202.5399932861328,197.6499938964844
2024-07-19,195.02999877929688,198.58999633789065,197.00999450683597
2024-07-22,194.22999572753903,197.25,196.3999938964844
2024-07-23,196.75999450683597,199.47999572753903,195.1100006103516
2024-07-24,194.3800048828125,198.44000244140625,196.5399932861328
2024-07-25,190.8800048828125,197.5500030517578,192.6199951171875
2024-07-26,193.3000030517578,198.22999572753903,196.5800018310547
2024-07-29,191.8300018310547,194.75,193.7400054931641
2024-07-30,193.7899932861328,195.5399932861328,192.7100067138672
2024-07-31,194.3500061035156,197.1199951171875,195.3699951171875
2024-08-01,197.25,198.1000061035156,194.82000732421875
2024-08-02,196.4499969482422,197.0200042724609,196.8699951171875
2024-08-05,190.5800018310547,194.05999755859372,188.8000030517578
2024-08-06,196.3500061035156,197.8000030517578,190.58999633789065
2024-08-07,190.38999938964844,196.0,190.0
2024-08-08,199.7899932861328,200.2700042724609,190.0
2024-08-09,182.19000244140625,187.8000030517578,174.2100067138672
2024-08-12,188.0500030517578,191.66000366210935,183.2400054931641
2024-08-13,194.58999633789065,195.25,189.0
2024-08-14,191.5399932861328,196.47999572753903,193.2400054931641
2024-08-15,195.02999877929688,196.8999938964844,194.4600067138672
2024-08-16,193.50999450683597,196.94000244140625,195.1199951171875
2024-08-19,195.9199981689453,198.1100006103516,194.57000732421875
2024-08-20,182.47000122070312,193.4499969482422,192.72999572753903
2024-08-21,185.8000030517578,186.5800018310547,183.8500061035156
2024-08-22,185.66000366210935,186.75999450683597,186.75999450683597
2024-08-23,185.0399932861328,188.25,187.1300048828125
2024-08-26,180.69000244140625,185.16000366210935,185.0399932861328
2024-08-27,192.5800018310547,196.5200042724609,186.1499938964844
2024-08-28,204.4199981689453,205.4600067138672,191.7700042724609
2024-08-29,205.1499938964844,207.3000030517578,205.9199981689453
2024-08-30,202.7700042724609,209.22000122070312,207.9900054931641
2024-09-03,206.69000244140625,206.77999877929688,202.0
2024-09-04,212.50999450683597,219.5200042724609,206.6300048828125
2024-09-05,216.1100006103516,221.6100006103516,213.5500030517578
2024-09-06,214.75,217.72000122070312,216.1000061035156
2024-09-09,219.1300048828125,222.0,218.1199951171875
2024-09-10,226.5,227.25999450683597,217.82000732421875
2024-09-11,227.72999572753903,229.7700042724609,224.97999572753903
2024-09-12,230.4499969482422,232.55999755859372,227.75
2024-09-13,233.8699951171875,234.7100067138672,230.4499969482422
2024-09-16,233.88999938964844,236.6199951171875,234.05999755859372
2024-09-17,235.5399932861328,243.97999572753903,235.0
2024-09-18,236.1100006103516,237.17999267578125,235.5399932861328
2024-09-19,237.67999267578125,239.44000244140625,239.42999267578125
2024-09-20,236.5800018310547,237.94000244140625,235.2899932861328
2024-09-23,238.97000122070312,239.08999633789065,237.3999938964844
2024-09-24,239.00999450683597,242.69000244140625,239.8300018310547
2024-09-25,238.8000030517578,240.8600006103516,239.97999572753903
2024-09-26,235.42999267578125,239.6499938964844,239.1999969482422
2024-09-27,232.02999877929688,238.3999938964844,236.9600067138672
2024-09-30,232.75,233.44000244140625,232.67999267578125
2024-10-01,234.55999755859372,235.33999633789065,233.7700042724609
2024-10-02,232.6300048828125,235.22999572753903,234.19000244140625
2024-10-03,229.9900054931641,233.94000244140625,231.72000122070312
2024-10-04,229.94000244140625,232.2100067138672,231.2899932861328
2024-10-07,227.7899932861328,228.8999938964844,228.77999877929688
2024-10-08,229.3300018310547,231.80999755859372,229.0800018310547
2024-10-09,231.83999633789065,231.9600067138672,229.32000732421875
2024-10-10,231.1999969482422,232.47000122070312,229.83999633789065
2024-10-11,233.1000061035156,236.42999267578125,232.25999450683597
2024-10-14,232.50999450683597,234.17999267578125,233.72999572753903
2024-10-15,230.07000732421875,234.02999877929688,231.7100067138672
2024-10-16,230.6000061035156,232.8000030517578,230.9499969482422
2024-10-17,229.1300048828125,231.6999969482422,230.63999938964844
2024-10-18,236.58999633789065,236.8699951171875,229.7700042724609
2024-10-21,236.47999572753903,239.08999633789065,236.58999633789065
2024-10-22,236.6000061035156,237.2400054931641,236.47999572753903
2024-10-23,234.83999633789065,238.72000122070312,235.58999633789065
2024-10-24,237.6300048828125,238.5200042724609,235.41000366210935
2024-10-25,233.6300048828125,238.6999969482422,237.08999633789065
2024-10-28,233.3699951171875,236.8600006103516,235.91000366210935
2024-10-29,232.3699951171875,234.0399932861328,231.50999450683597
2024-10-30,230.5800018310547,232.3999938964844,230.8600006103516
2024-10-31,231.52999877929688,231.97000122070312,229.6100006103516
2024-11-01,235.6100006103516,236.7400054931641,230.07000732421875
2024-11-04,237.44000244140625,240.77999877929688,236.0200042724609
2024-11-05,241.32000732421875,242.1100006103516,236.88999938964844
2024-11-06,239.3000030517578,248.5500030517578,248.5500030517578
2024-11-07,244.97999572753903,245.1699981689453,237.3500061035156
2024-11-08,268.0,275.5199890136719,256.8999938964844
2024-11-11,275.70001220703125,279.3999938964844,268.1600036621094
2024-11-12,275.1000061035156,276.0599975585937,275.69000244140625
2024-11-13,269.0599975585937,276.57000732421875,275.4700012207031
2024-11-14,261.1600036621094,267.5799865722656,266.4599914550781
2024-11-15,260.1199951171875,264.7099914550781,261.0
2024-11-18,260.67999267578125,263.92999267578125,260.1000061035156
2024-11-19,261.989990234375,265.2699890136719,259.3900146484375
2024-11-20,266.5799865722656,267.04998779296875,262.239990234375
2024-11-21,262.0,267.42999267578125,267.42999267578125
2024-11-22,262.92999267578125,264.57000732421875,262.8299865722656
2024-11-25,266.5799865722656,267.3299865722656,264.82000732421875
2024-11-26,266.4200134277344,269.1400146484375,265.9100036621094
2024-11-27,266.9200134277344,272.5599975585937,267.57000732421875
2024-11-29,266.7799987792969,267.8999938964844,266.3599853515625
2024-12-02,266.489990234375,270.19000244140625,267.5799865722656
2024-12-03,269.6600036621094,270.5599975585937,265.1300048828125
2024-12-04,269.2099914550781,270.8099975585937,270.010009765625
2024-12-05,267.5799865722656,275.3399963378906,269.0
2024-12-06,265.4599914550781,270.2900085449219,267.3900146484375
2024-12-09,265.1199951171875,267.1000061035156,266.0899963378906
2024-12-10,274.7900085449219,278.7099914550781,266.8800048828125
2024-12-11,273.4700012207031,279.3900146484375,277.4100036621094
2024-12-12,271.7300109863281,279.7699890136719,276.4200134277344
2024-12-13,269.3399963378906,272.7699890136719,271.75
2024-12-16,265.5,271.17999267578125,267.6000061035156
2024-12-17,263.3500061035156,265.6700134277344,262.989990234375
2024-12-18,256.44000244140625,262.6700134277344,261.8800048828125
2024-12-19,256.5599975585937,259.0400085449219,256.5
2024-12-20,266.57000732421875,270.70001220703125,256.5599975585937
2024-12-23,263.3299865722656,266.44000244140625,264.82000732421875
2024-12-24,263.2300109863281,264.1700134277344,263.9100036621094
2024-12-26,265.67999267578125,266.4200134277344,261.260009765625
2024-12-27,265.1199951171875,266.5899963378906,262.6099853515625
2024-12-30,263.3599853515625,264.239990234375,262.5599975585937
2024-12-31,261.07000732421875,265.4599914550781,264.75
2025-01-02,256.8500061035156,263.8299865722656,259.8399963378906
2025-01-03,266.29998779296875,267.6700134277344,258.0
2025-01-06,268.4100036621094,269.94000244140625,267.6499938964844
2025-01-07,265.6499938964844,269.6300048828125,267.8399963378906
2025-01-08,270.3599853515625,271.3500061035156,264.1700134277344
2025-01-10,271.8299865722656,274.45001220703125,268.17999267578125
2025-01-13,267.989990234375,271.32000732421875,271.32000732421875
2025-01-14,267.0400085449219,271.1300048828125,268.8999938964844
2025-01-15,264.3800048828125,270.7699890136719,270.1099853515625
2025-01-16,272.8599853515625,275.3299865722656,264.2200012207031
2025-01-17,275.8099975585937,278.5299987792969,275.67999267578125
2025-01-21,276.0799865722656,282.8599853515625,279.0199890136719
2025-01-22,278.8900146484375,279.67999267578125,275.1199951171875
2025-01-23,277.20001220703125,279.9700012207031,279.2300109863281
2025-01-24,280.3500061035156,280.7300109863281,275.2799987792969
2025-01-27,275.8999938964844,282.8699951171875,280.4100036621094
2025-01-28,275.9700012207031,282.8699951171875,275.8500061035156
2025-01-29,277.1099853515625,277.9200134277344,276.8800048828125
2025-01-30,280.0299987792969,286.3900146484375,278.1400146484375
2025-01-31,278.3800048828125,284.6199951171875,277.3999938964844
2025-02-03,278.8999938964844,281.3500061035156,276.1700134277344
2025-02-04,278.4800109863281,280.3999938964844,279.2699890136719
2025-02-05,284.70001220703125,287.0,279.6700134277344
2025-02-06,287.6700134277344,288.04998779296875,284.7799987792969
2025-02-07,283.0799865722656,289.4599914550781,287.6700134277344
2025-02-10,285.3399963378906,286.5899963378906,284.3599853515625
2025-02-11,284.260009765625,287.0,284.1600036621094
2025-02-12,279.54998779296875,282.9200134277344,280.2200012207031
2025-02-13,282.1199951171875,282.9800109863281,281.32000732421875
2025-02-14,280.5599975585937,283.989990234375,281.67999267578125
2025-02-18,280.7099914550781,284.3999938964844,280.20001220703125
2025-02-19,283.67999267578125,288.95001220703125,280.8900146484375
2025-02-20,288.2900085449219,288.92999267578125,281.6099853515625
2025-02-21,282.79998779296875,286.6600036621094,276.3500061035156
2025-02-24,283.4800109863281,287.70001220703125,283.69000244140625
2025-02-25,266.67999267578125,283.3299865722656,282.57000732421875
2025-02-26,270.6400146484375,272.42999267578125,266.1099853515625
2025-02-27,267.0899963378906,270.79998779296875,269.510009765625
2025-02-28,272.2699890136719,272.7300109863281,267.8900146484375
2025-03-03,272.6400146484375,279.6400146484375,272.8699951171875
2025-03-04,269.70001220703125,273.2200012207031,272.1199951171875
2025-03-05,270.8099975585937,271.8800048828125,269.3699951171875
2025-03-06,259.6700134277344,269.5799865722656,269.5799865722656
2025-03-07,251.80999755859372,260.9100036621094,259.4800109863281
2025-03-10,237.05999755859372,249.6199951171875,249.6199951171875
2025-03-11,245.3500061035156,248.4900054931641,238.0200042724609
2025-03-12,248.3800048828125,255.6300048828125,250.2700042724609
2025-03-13,244.6699981689453,247.5800018310547,247.5800018310547
2025-03-14,255.44000244140625,257.25,247.66000366210935
2025-03-17,261.6300048828125,262.4800109863281,254.6999969482422
2025-03-18,260.4700012207031,264.8299865722656,261.25
2025-03-19,265.82000732421875,266.8900146484375,261.42999267578125
2025-03-20,265.3900146484375,269.69000244140625,264.5
2025-03-21,268.32000732421875,268.9700012207031,263.4700012207031
2025-03-24,274.0400085449219,274.8500061035156,272.3800048828125
2025-03-25,272.7099914550781,276.1300048828125,274.6199951171875
2025-03-26,264.8800048828125,275.4200134277344,272.4700012207031
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Indicator data:
date,20-day,close
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2025-04-14,258.6743711605694,255.47000122070312
2025-04-15,258.4606208286848,256.42999267578125
2025-04-16,257.72437081905184,250.72999572753903
2025-04-17,256.6839548412143,246.8000030517578
2025-04-21,254.95881698245282,238.57000732421875
2025-04-22,253.9170252957869,244.0200042724609
2025-04-23,253.20969007648952,246.4900054931641
2025-04-24,253.79733910566313,259.3800048828125
2025-04-25,254.45568694846457,260.7099914550781
2025-04-28,254.93800143086526,259.5199890136719
2025-04-29,254.58866836816009,251.2700042724609
2025-04-30,254.36974693177655,252.2899932861328
2025-05-01,253.97739008113118,250.25
2025-05-02,254.26621100346392,257.010009765625
2025-05-05,254.69704886455517,258.7900085449219
2025-05-06,255.09447231718684,258.8699951171875
2025-05-07,255.972141387797,264.3099975585937
2025-05-08,256.07003268419726,257.0
2025-05-09,261.2700308502484,310.6700134277344
2025-05-12,266.54621966715183,316.6700134277344
2025-05-13,271.1094360279067,314.4599914550781
2025-05-14,275.89996627878315,321.4100036621094
2025-05-15,280.2923493963916,322.0199890136719
2025-05-16,284.52641135864,324.75
2025-05-19,288.461038499521,325.8399963378906
2025-05-20,292.17617780630025,327.4700012207031
2025-05-21,295.25463706284313,324.5
2025-05-22,297.7065763901914,321.0
2025-05-23,299.95928200556006,321.3599853515625
2025-05-27,302.5003041620246,326.6400146484375
2025-05-28,304.5050359364002,323.54998779296875
2025-05-29,306.347414047554,323.8500061035156
2025-05-30,308.1267078315296,325.0299987792969
2025-06-02,309.7336880380506,325.0
2025-06-03,311.02000253293863,323.239990234375
2025-06-04,311.8000014779043,319.2099914550781
2025-06-05,312.3104778764,317.1600036621094
2025-06-06,312.2590027466164,311.7699890136719
2025-06-09,311.63052664333,305.6600036621094
2025-06-10,310.4019061045679,298.7300109863281
2025-06-11,309.62458078359714,302.239990234375
2025-06-12,309.05271548203433,303.6199951171875
2025-06-13,308.6315049487751,304.6300048828125
2025-06-16,308.4370755572623,306.5899963378906
2025-06-17,308.05164118499323,304.3900146484375
2025-06-18,307.4552952192721,301.7900085449219
2025-06-20,307.0452665218637,303.1499938964844
2025-06-23,307.1047662271847,307.6700134277344
2025-06-24,307.4662164814037,310.8999938964844
2025-06-25,307.3484826247298,306.2300109863281
2025-06-26,307.5848163340189,309.8299865722656

Answer: 27.0