# Find the mean, mode and median for the following data set given the mid-values and their associated frequencies.Mid Value- 15,20,25,30,35,40,45,50,55 Frequencies - 2,22,19,14,3,4,6,1,1

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### 2 Answers

Let's put this in a different format to make the data easier to read:

Mid Value (Frequency)

15 (2)

20 (22)

25 (19)

30 (14)

35 (3)

40 (4)

45 (6)

50 (1)

55 (1)

Now that we have these numbers parsed out, let's start with our set of averages (mean, median, and mode) For information on each of these, see the links below.

**Find the mode**

To find the mode, we simply select the mid value with the highest frequency:

**Mode = 20**

Bam! We're done with that. Moving on.

**Find the mean**

This is a little more difficult, but it's not bad. We first need to determine how many total samples (n) we have. To do this, we simple add the frequencies:

``

So, we have 72 total samples.

Now, we need to calculate the sum of each midvalue from our data. Recall, the frequency is the number of times we hit a particular midvalue, so to find the sum of all midvalues, we'll simply multiply each midvalue by its frequency and take the sum (T):

``

``

Now, to get the mean, we just divide T by n:

Mean``

Our **mean is 27.8**

**Finding the median**

To find the median, we must find the middle value by counting the samples from the lowest midvalue up until we reach halfway through the sample. In our case, because we have an even number of samples, we must take the mean of the midvalue at sample numbers 36 and 37.

To find what midvalues are at samples 36 and 37, we look at the frequencies. We know the first 2 samples are at midvalue 15. The next 22 (sample numbers 3-24) are at midvalue 20. The next 19 samples (sample numbers 25-43) are at midvalue 25.

If you'll notice, that last set of 19 samples contains the two samples we were looking for to determine the median (#36 and #37). Both samples, based on our analysis have a midvalue of 25. Their mean (and therefore, the median of our whole data set) is then 25.

**So, we have our median: 25.**

I hope that helps!

**Sources:**

15-2

20 -22

25 -19

30 -14

35 -3

40 -4

45 -6

50 -1

55 -1

mode= 20

we have 72 numbers in total (add up all the frequencies), so add all the mid values and divide by 72

there are 72 numbers 72/2 = 36

the two 36 numbers are the median meaning 25 and 25, add them and divide by 2 to get median

median=25