Question

The arithmetic mean and standard deviation of a series of 20 items were computed as 20 cm and 5 cm respectively.While calculating test,an item 13 cm was misread as 30 calculate mean and standard deviation when misread items is omitted. pls send solution by showing steps

Answer 1

Answer: n=20     mean=20    standard deviation=5   variance=(5)²=25

mean = sum of observations / no. of observation

20   = Σx/20

400 = Σx

and variance = Σx²/20 - (mean)²

25 = Σx²/20 - (20)²

Σx² = 20(25+400)

Σx² = 20*425

Σx² = 8500

Correct Σx² = 8500-(30)² = 7600

Correct Σx = 400-30 = 370

Correct mean = Correct Σx / 19

                        = 370/19

                        = 19.47

Correct variance = Correct Σx²/19 - (Correct mean)²

                            = 7600/19 - (19.47)²

                            = 400 - 379.08

                            = 20.92

Correct Standard deviation = √20.92

                                              4.57

Hope it helps!

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