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CAHSEE Math 1.5 Statistics, Data, and Probability I 234 Views


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Description:

Statistics, Data, and Probability I: Drill Set 1, Problem 5. Which should be used to represent her time?

Language:
English Language

Transcript

00:03

Okay, let's get down to the shmoopy question.

00:06

Tamara, a runner in her high school track team, posted lap times of 24, 18, 21, 15,

00:13

and 18 seconds on her practice runs.

00:15

If her coach allowed her to pick the mean, median, or mode of this set for evaluation

00:20

of her fastest times, which should she use to represent her time?

00:26

Here are the possible answers:

00:33

Clearly Tamara needs to work on her pacing.

00:35

Like... come on... a 15 second lap and a 24 seconder?

00:38

What is she... downing Big Macs between laps?

00:41

Okay... now what's this... semi-weird question asking?

00:44

Well, 3 things, really... all involving vocab words we have to know:

00:49

That's mean... median... and mode.

00:52

And there's a curve ball thrown in here...

00:54

in that we want the lowest number...

00:57

The lowest number represents the shortest time it took Tammy-pie to run her lap.

01:02

Smaller is better.

01:04

So there are 3 parts to this problem.

01:07

First, we calculate the mean or average... which is:

01:10

24 + 18 + 21 + 15 + 18, which totals 96.

01:15

Divide the 96 by 5, since we're averaging 5 elements...

01:19

...and we get 19.2 as the mean.

01:22

So Tamara's mean time based on this assessment of her fine athletic field efforts is 19.2.

01:27

We're a third of the way there. Second, we calculate the median.

01:31

Median is just a fancy way of saying "the middle."

01:34

Once we order the numbers from smallest to biggest...

01:38

...we can see that the middle number is 18.

01:41

So the median has beaten out the mean by 1.2 seconds.

01:45

But we have a third calculation we need to apply... mode.

01:49

In other words, what number occurs most frequently?

01:52

Doesn't matter how big it is. For example, if we're looking for the mode among 99,

01:56

98, 97, 96, 2 and 2...

01:58

Our mode is 2. Score one for the little guy. Right. So what's the mode here? 18.

02:05

It appears we have a tie.

02:07

Median and mode... going to sudden death...

02:09

So the answer is D, "either"...

02:12

...that is, the median and mode are both 18.

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