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The table shows some information about the lifetimes, t, in hours, of some lightbulbs.
Frequency
Lifetime
25 47
50 < t ≤ 100
86
100 45
150 < t ≤ 200
36
200 0
250 37
300 < t ≤ 350
50
Estimate the mean lifetime of a bulb.
Give your answer rounded to 2 DP.
hours

Sagot :

MrRoyalidn

The estimated mean lifetime of a bulb of 154.69

How to estimate the mean lifetime of a bulb?

The table is given as:

Lifetime                Frequency

25 < t ≤ 50             47

50 < t ≤ 100            86

100 < t ≤ 150          45

150 < t ≤ 200         36

200 < t ≤ 250        0

250 < t ≤ 300       37

300 < t ≤ 350      50

Calculate the midpoint using:

x = (Lower +Upper)/2

So, we have:

Lifetime                Frequency

37.5                        47

75                           86

125                        45

175                        36

225                        0

275                       37

325                      50

The mean value is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{37.5 * 47 + 75 * 86 + 125 * 45 + 175 * 36 + 225 * 0 + 275 * 37 + 325 * 50}{47 + 86 + 45 + 36 + 0 + 37 + 50}[/tex]

Evaluate

[tex]\bar x = \frac{46562.5}{301}[/tex]

Divide

[tex]\bar x = 154.69[/tex]

Hence, the estimated mean lifetime of a bulb of 154.69

Read more about mean at:

https://brainly.com/question/14532771

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