I need help finding the mode, median and mean of this frequency table

[somavera7]

I know what the mode, median and mean are but I have no idea how to calculate them using the information from this table.

If the frequency numbers were smaller, I would probably try to solve this by writing out each age group the amount of times represented by the frequency. But these are large numbers, so it would take me forever to write them out.

What is the best way to solve this problem? Can you explain to me the steps for solving it?



Thank you!

 

[Steven G]

In the data list you need to find the middle number. For example, in 90-94 the middle number (or average) is 92. So you find the mean, mode, median using 92.

Now to find the mean you add up all the numbers and divide by the number of numbers.

The mean will be ( 62+62 + 67+ 72+72+72+72 + ...)/(total number of numbers) = ( 2*62 + 67 + 4*72 + ...)/(total number of numbers)

So instead of adding on to the sum 97 17 times, why not just add on 97*17. That is a lot easier, isn't it. Now how many numbers are there? You need this to find the mean.

Suppose there are 101 numbers. Which position number or numbers is the middle? Can you find the middle number That will be the median.

The mode should be obvious. What is the definition of the mode.

If you have any questions then post back.

 

[somavera7]

In the data list you need to find the middle number. For example, in 90-94 the middle number (or average) is 92. So you find the mean, mode, median using 92.

Now to find the mean you add up all the numbers and divide by the number of numbers.

The mean will be ( 62+62 + 67+ 72+72+72+72 + ...)/(total number of numbers) = ( 2*62 + 67 + 4*72 + ...)/(total number of numbers)

So instead of adding on to the sum 97 17 times, why not just add on 97*17. That is a lot easier, isn't it. Now how many numbers are there? You need this to find the mean.

Suppose there are 101 numbers. Which position number or numbers is the middle? Can you find the middle number That will be the median.

The mode should be obvious. What is the definition of the mode.

If you have any questions then post back.

Thank you for the answer!

But I need some more detail in order to understand this.

From reading your post, I think you're saying to find the mean like this.

62 * 2 = 124
67 * 1 = 67
72 * 4 = 288
77 * 4 = 308
82 * 5 = 410
88 * 12 = 1056
92 * 14 = 1288
97 * 17 = 1649
102 * 12 = 1224

These numbers added together come out to 6414

The table shows 9 age groups. So, the mean would be 6414 / 9 = 712.67

Hopefully I have calculated the mean correctly as this question asks.


The mode is the number that appears the most, so I'm thinking it is 97, because that row has a frequency of 17.


However, I'm still unsure about how to find the median of this data. How can I find the middle number(s) when there are so many numbers?

 

[HallsofIvy]

Thank you for the answer!

But I need some more detail in order to understand this.

From reading your post, I think you're saying to find the mean like this.

62 * 2 = 124
67 * 1 = 67
72 * 4 = 288
77 * 4 = 308
82 * 5 = 410
88 * 12 = 1056
92 * 14 = 1288
97 * 17 = 1649
102 * 12 = 1224

These numbers added together come out to 6414

The table shows 9 age groups. So, the mean would be 6414 / 9 = 712.67

Hopefully I have calculated the mean correctly as this question asks.

You understand that the "mean" is an average, don't you?
All the ages shown are less than 104. Do you really think the average age of these people is "712.67"??

You got 6414 by multiplying the average age of each group by the number of people in the that group and adding so that reflects the total of all the ages of all the people. Divide by the number of people, not the number of groups!

The mode is the number that appears the most, so I'm thinking it is 97, because that row has a frequency of 17.

Yes, although it would be a little better to say that any number from 95 to 99 is a mode.

However, I'm still unsure about how to find the median of this data. How can I find the middle number(s) when there are so many numbers?

Well, you are going to have to do some work! I have already said that to find the mean you have to divide 6414 by the number of people. So you have to calculate the total number of people- that is 2+ 1+ 4+ 4+ 5+ 12+ 14+ 17+ 12. What is half of that? Now add those same numbers, 2+ 1+ 4... until you get to that half. Where do you stop?

 

[Dr.Peterson]

However, I'm still unsure about how to find the median of this data. How can I find the middle number(s) when there are so many numbers?

Imagine that you did what you initially said you would do with smaller frequencies, and wrote out all the numbers.

How many would there be?

How many would be to the left of the median?

Which group would that value be within? (Add up frequencies cumulatively.)

By the way, the question asks for more precision than is possible for mode and median, since grouping loses a lot of detail. It is possible that you were taught a formula for an estimated mode and median, which allows you to give an answer other than the midpoint of a group; but if you were, then you would not be asking this the way you did.

 

[Steven G]

There are many more than 9 numbers in total. Sure there are 9 distinct (different) numbers but for example there were 17 scores of 97. So there must be at least a total of 17 scores! Think about how many numbers you would be adding up if you did not use multiplication!