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## AP®︎/College Statistics

### Course: AP®︎/College Statistics > Unit 3

Lesson 1: Measuring center in quantitative data# Median in a histogram

Worked example from Khan Academy finding the interval in a histogram containing the media of a data set.

## Want to join the conversation?

- I am frustrated with the measuring center quantitative data scoring for completion of calculating the median. My answers are correct, but the dialog box shows I need to "try again" or more to the answer is requested. I had no problems with practice calculating the mean. What am I doing wrong? I sent my feedback on the issue, but seem to be getting nowhere.(17 votes)
- At1:17how would the 25th and 26th be the two data points if the number of consecutive days is 50?(7 votes)
- since 50 is an even number, the median (or the middle number of days) is going to be the two middle values.

Consider writing out all the number of days from 1-50, and try to find the median values.(7 votes)

- Where and how did he get the 23 lowest? I was really thrown off. I've tried re-watching it multiple times but I still cant seem to figure it out.(4 votes)
- The histogram tells us that out of the 50 days, there were...

...2 days when Miguel slept between 6 and 6.5 hours.

...9 days when he slept between 6.5 and 7 hours.

...12 days when he slept between 7 and 7.5 hours.

...12 days when he slept between 7.5 and 8 hours.

...11 days when he slept between 8 and 8.5 hours.

...2 days when he slept between 8.5 and 9 hours.

...2 days when he slept between 9 and 9.5 hours.

This means that there were

2 + 9 + 12 = 23 days when Miguel got less than 7.5 hours of sleep, which are also the 23 days when he got the least amount of sleep because all the other days he got 7.5 hours of sleep or more.(7 votes)

- hey how does this help in life(4 votes)
- @robitaille.alexandre it helps in life because when you are trying to find the average of say, how much you spend in a month, it is easy to calculate.(5 votes)

- Mode may also be estimated from a histogram. However, what will be the mode in the above-mentioned example? There are two ADJACENT bars with equal heights. Theoretically, this is a bi-modal set of grouped data. How do we estimate the modes graphically in such a case?(2 votes)
- i have a hard time in this mode for example 2951275?(2 votes)
- I'm confused... why the median is calculated from the amount of days tracked by Miguel instead of doing it from the number of hours he slept?(2 votes)
- I'm confused. I'm doing the grade 6 unit test and it asks "In which interval is the median distance?". He doesn't talk about intervals in grade 6. In fact the median in a histogram video above is not in the grade 6 data and statistics unit. What grade is this?(2 votes)
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Question(2 votes) - i have confusion in finding median(1 vote)
- The mean is all the numbers added up together, then divided by the number of numbers you added up(3 votes)

## Video transcript

- [Narrator] Miguel tracked
how much sleep he got for 50 consecutive days and
made a histogram of the results. Which interval contains
the median sleep amount? And so they're saying is it
this interval on the histogram from six to 6.5, or this one
or this one, or any of these. Which of these intervals
contain the median. Pause this video and see
if you can figure that out. All right now let's work
through this together. And let's just remind ourselves
how we find the median. If I had the data points 11,
nine, seven, three, and two, the way that we find the
median is we can order it from least to greatest or
actually you could do it from greatest to least, but
let's do least to greatest. So two, three, seven, nine, 11. And the median would be the middle number. And I have a clear middle number because I have five data points. If I have an even number of data points, I still would want to order
them from least to greatest, so let's say that I have a
one, one, three, and a seven. But here, you don't have a clear middle. So the median would be the
mean of the middle two numbers. So in this situation, Miguel has an even number of data points. So the median would be the mean of the 25th and 26th data point. These would be the middle two data points. So which interval here contains the 25th and the 26th data point? Well, we can start at the bottom. So we have, actually let's
just look at each interval and think about how many
data points they have in it. This one has two, this one has nine, this one has 12, and I'm just reading out how many data points there are
in each of these intervals. This one has 12, this one
has 11, see that there. This one has two and this one has two. So if we look at just this,
we have the two lowest, if we look at the two
bottom intervals combined we have the 11 lowest. If we look at the three bottom intervals, we have the 11 plus, 12,
you have the 23 lowest. So this is the 23 lowest data points. And so the 24th, 25th, 26th, the next 12 data points starting from the bottom, starting from the lowest are going to be in this next interval here. And we care about the 25th and the 26th, so they're definitely going
to be in this interval from 7.5 hours of sleep
to eight hours of sleep.