b) Estimated mean = 4.64 Estimated variance = 6.87 Estimated standard deviation = = 2.62 m(midpoint) f(x) mf(x) m− (m−)2 (m−)2f(x) 1.5 20 30 9.86 197.19 −3.14 4.5 24 108 0.02 0.47 −0.14 7.5 17 127.5 2.86 8.18 139.05 10.5 3 31.5 5.86 34.34 103.02 totals 64 297 439.73 = 297/64  439.73/64 = 4.64 = 6.87 73. a) class midpoint frequency 0 to under 5 2.5 34 5 to under 10 7.5 30 b) Estimated mean = 4.84 Estimated variance = 6.23 Estimated standard deviation = = 2.50 m(midpoint) f(x) mf(x) m− (m−)2 (m−)2f(x)
b) Estimated mean = 4.64 Estimated variance = 6.87 Estimated standard deviation = = 2.62 m(midpoint) f(x) mf(x) m− (m−)2 (m−)2f(x) 1.5 20 30 −3.14 9.86 197.19 4.5 24 108 −0.14 0.02 0.47 7.5 17 127.5 2.86 8.18 139.05 10.5 3 31.5 5.86 34.34 103.02 totals 64 297 439.73  = 297/64 439.73/64 = 4.64 = 6.87 73. a) class midpoint frequency 0 to under 5 2.5 34 5 to under 10 7.5 30 b) Estimated mean = 4.84 Estimated variance = 6.23 Estimated standard deviation = = 2.50 m(midpoint) f(x) mf(x) m− (m−)2 (m−)2f(x)