Bursting Pressure | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 | |

Number of bags manufactured by | A | 2 | 9 | 29 | 54 | 11 | 5 |

B | 9 | 11 | 18 | 32 | 27 | 13 |

Which set of bags has more uniform pressure? If price are the same, Which manufacture’s bags would be preferred by buyer? Use appropriate statistical tool

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Login Now**Range, interquartile range, standard deviation. and variance** are the three commonly used measures of dispersion.

**Solution:**

Let X be the mid value so that \(d^{”} = \frac{17.45}{5}\). Let f and f^{‘} be the number of bags of manufactures A and B respectively.

Class | x | \(d^{‘} = \frac{x – 17.45}{5}\) | f | f^{‘} |
fd^{‘} |
fd^{‘2} |
f^{‘}d^{‘} |
f^{‘}d^{‘2} |

5-9.9 | 7.45 | -2 | 2 | 9 | -4 | 8 | -18 | 36 |

10-14.9 | 12.45 | -2 | 9 | 11 | -9 | 9 | -11 | 11 |

15-19.9 | 17.45 | 0 | 29 | 18 | 0 | 0 | 0 | 0 |

20-24.9 | 22.45 | 1 | 54 | 32 | 54 | 54 | 32 | 32 |

25-29.9 | 27.45 | 2 | 11 | 27 | 22 | 22 | 54 | 108 |

30-34.9 | 32.45 | 3 | 5 | 13 | 15 | 15 | 39 | 117 |

Σd^{‘} = 3 |
N=10 | N^{‘} = 110 |
Σfd^{‘}=78 |
Σfd^{‘2}=160 |
Σf^{‘}d^{‘} = 96 |
Σf^{‘}d^{‘2}=304 |

For manufacture A:

\(Mean(\bar{X}_A) = A + \frac{\sum fd^{‘}}{N} \times h\)

= \(17.45 + \frac{78}{100} \times 5\)

= 21

Standard Deviation(σ_{A}) = \(h\sqrt{\frac{\sum fd^{‘2}}{N} – \left ( \frac{\sum fd^{‘}}{N} \right )^2}\)

= \(5 \times \sqrt{\frac{160}{110} – \left ( \frac{78}{110} \right )^2}\)

= 5 x 0.975

= 4.875

Covariance(A) = \(\frac{σ_{A}}{\bar{X}_{A}} \times 100%\)

= \(\frac{4.875}{21} \times 100%\)

= 23.2%

For manufacture B:

\(Mean(\bar{X}_B) = A + \frac{\sum fd^{‘}}{N} \times h\)

= \(17.45 + \frac{96}{100} \times 5\)

= 21.8

Standard Deviation(σ_{A}) = \(h\sqrt{\frac{\sum fd^{‘2}}{N} – \left ( \frac{\sum fd^{‘}}{N} \right )^2}\)

= \(5 \times \sqrt{\frac{204}{110} – \left ( \frac{96}{110} \right )^2}\)

= 5 x 1.41

= 7.05

Covariance(A) = \(\frac{σ_{A}}{\bar{X}_{A}} \times 100%\)

= \(\frac{7.05}{21.8} \times 100%\)

= 32.34%

Since, the cofficient of variation for A is less than that for B, the set of bags manufactured by A has more uniform pressure.Hence, the buyer would perfer to buy bags manufactured by A.

**Another Method:**

Brusting Pressure |
M |
A |
B |
AM |
BM |

5-10 | 7.5 | 2 | 9 | 15 | 67.5 |

10-15 | 12.5 | 9 | 11 | 112.5 | 137.5 |

15-20 | 17.5 | 29 | 18 | 507.5 | 315 |

20-25 | 22.5 | 54 | 32 | 1215 | 720 |

ΣA = 94 | ΣB = 70 | ΣAM = 1850 | ΣBM = 1240 |

Brusting pressure of Polythene A = \(\frac{\sum AM}{\sum A}\)

= \(\frac{1850}{94}\)

= 19.68

Brusting pressure of Polythene B = \(\frac{\sum BM}{\sum B}\)

= \(\frac{1240}{70}\)

= 17.68

Since, the brusting pressure of polythene A is greater than of polythene B. So, Buyers perfers the polythene A.

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