Statistical Properties of Ordered and Unordered Numerical Sets
Statistical Properties of Ordered and Unordered Numerical Sets
Secondary 4
Two brands of light bulbs were tested for their reliability. \(10\) light bulbs of each brand were randomly selected and they were switched on for a number of days until they blew out. The number of days that each bulb lasted was then noted. The results are given below.
| Brand | Number of days bulb lasted | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| \(A\) | \(101\) | \(100\) | \(99\) | \(105\) | \(102\) | \(101\) | \(98\) | \(100\) | \(97\) | \(97\) |
| Brand | Number of days bulb lasted | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| \(B\) | \(95\) | \(101\) | \(100\) | \(103\) | \(92\) | \(107\) | \(106\) | \(94\) | \(98\) | \(104\) |
- For Brand \(A\), find
- the mean number of days the light bulbs lasted,
- the standard deviation of the number of days, correct to \(3\) significant figures.
- For Brand \(B\), find
- the mean number of days the light bulbs lasted,
- the standard deviation of the number of days, correct to \(3\) significant figures.
- Which brand of light bulb is more reliable? Give a reason for your answer.
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Answer:(a)(i) 100 days. (ii) 2.32 days (3 s.f.). (b)(i) 100 days. (ii) 4.90 days (3 s.f.). (c) Brand A is more reliable because its standard deviation is smaller.
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