Question

A study of the lifetime (in hours) for a certain brand of light bulb involved putting 10 light bulbs into operation and observing them for 1000 hours. Eight of the light bulbs failed during that period, and those lifetimes were recorded. The lifetimes of the two light bulbs still functioning after 1000 hours were recorded as 1000 . The resulting sample observations are below. 510 790 1000 330 910 840 580 1000 160 280 Which of the measures of center discussed in this section can be calculated?

Answer 1

Answer:

Step-by-step explanation:

Hello!

There are three values of central tendency you can calculate using the given data, the mean, X[bar], the median, Me, and the mode, Md.

You have the information of the lifetime in hs of 10 lightbulbs that lasted at most 1000hs.

510 790 1000 330 910 840 580 1000 160 280

Mean:

You can obtain this value by adding all observations and dividing it by the sample size:

X[bar]= ∑X/n= (510 + 790 + 1000 + 330 + 910 + 840 + 580 + 1000 + 160 + 280)/10= 5500/10= 550 hs

The average lifetime of the lightbulbs is 550 hs

Median:

The median is the value of the variable that divides the sample in exactly 50% (Also known as 2nd quantile) To obtain it you have to calculate it's position firs:

For even samples: PosMe= n/2= 10/2= 5 This means that the median is the 5th observation.

Now you have to order the observations from least to greatest and identify wich observation is the 5th.

160 280 330 510 580 790 840 910 1000 1000

Me= 580 hs

Mode:

The mode is the most observed value of the variable, i.e. the value of X with most absolute frequency.

In this case, there is only one value observed more than once, this value is the mode of the data set:

Md= 1000hs.

I hope it helps!