# AP Statistics 1.4 Exploring Data

AP Statistics 1.4 Exploring Data. For any collection of data, the mean must equal the median if the distribution is which of the following?

AP Statistics | Exploring Data |

Exploring Data | Summarizing Distributions of Univariate Data |

Language | English Language |

### Transcript

following right here potential answers last rites metric that's like

our last physical doctor with all righty So a pretty

general question here about plotting data where we need to

know the definition of two terms mean and media will

mean is the same as average while median is of

course that thing you drive over when you realize you

missed your left turn All right in this case it's

probably referring to the middle value in a set In

other words if we have the data set zero one

two three nine then the meaner average would be three

but our median would be too well Since we've already

identified a situation where the meaning the median would not

be equal we can go ahead and cross off option

e Well what about d mean can never equal the

median Well let's consider a situation in which we're plotting

the number of times You and four of your friends

have been born Hopefully you've all been born exactly once

We're not counting that time Your buddy martin had an

enlightening summer at church camp Okay so our data set

would be one juan juan one one the mean is

one but so is the media So d can't be

right So we know the mean can equal the median

sometimes Now to see whether our history graham would necessarily

skew left or right Well suppose we're plotting the number

of times three dogs have thrown up on the carpet

slugger has thrown up only once rico just twice But

bonzo seems to be making a habit of it having

thrown up in astounding two hundred ninety seven times and

lived to tell about it The meanest one hundred that's

three hundred but they're divided by three and that gets

you hundred see him take very clever Well the media

is just too because in the middle so here's an

example in the data skews left but the mean in

median are not necessarily equal so but by option a

we can easily imagine a scenario where the reverse is

true and the data skews right with unequal mean and

medium so we can cross off be using the same

logic which leaves only option c The main in the

median must be equal if the data is symmetric This

makes sense because with symmetric data each value on the

left will be a ce far away from the mean

and median as its corresponding value on the right Like

if we're plotting banana peels slipped on by five people

and the data looks like this are mean is six

and so is our media Well the number two is

four units away from the media and so is ten

well in the same way for an eight are both

two units away from the data's middle Both sides match

up or our symmetric well here's hoping the next time

you come upon a banana peel you don't uh skew 00:03:00.61 --> [endTime] downward Wait