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Travka [436]
2 years ago
5

Find the mean, median, and mode of the data with and without the outlier. 101, 110, 99, 100, 64, 112, 110, 111, 102

Mathematics
1 answer:
svetoff [14.1K]2 years ago
6 0

Answer:

Step-by-step explanation:

First step

Put the numbers in numerical order.

64 99 100 102 110 110 111 112  

Median

Median is the middle number. If the number of numbers is even then you take the middle 2 and average them.

This has 8 entries so you take the middle 2 and average them.

102 and 110 are the middle 2. They can be averaged.

(102 + 110)/2 = 212/2

212 / 2 = 106

The median is 106.

Mode

The mode is the entry with the most number that are the same.

110 is given twice. Nothing else is. So the mode is 110

Mean

The mean is the average. You add the eight numbers and divide by 8.

Sum = 64 + 99 +  100 +  102 +  110 +  110 +  111 +  112  

Sum = 808

Now divide by 8

Mean = 808/8

Mean = 101

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<h3>Answers:     x = -17  and   x = 64</h3>

====================================================

Explanation

Consider three scenarios:

  • A) The value of x is the smallest of the set (aka the min)
  • B) The value of x is the largest of the set (aka the max)
  • C) The value of x is neither the min, nor the max. So 8 < x < 39.

These scenarios cover all the possible cases of what x could be. It's either the min, the max, or somewhere in between the min and max.

--------------------

We'll start with scenario A.

If x is the min, then that must mean 39 is the max as it's the largest of the set {18, 36, 16, 39, 27, 8, 34}

The range is 56, so,

range = max - min

56 = 39 - x

56+x= 39

x = 39-56

x = -17  which is one possible answer

--------------------

If instead we go with scenario B, then x is the max and 8 is the min

range = max - min

56 = x - 8

56+8 = x

64 = x

x = 64 is the other possible answer

--------------------

Lastly, let's consider scenario C. If x is not the min or the max, then it's somewhere between the min 8 and max 39. in short, 8 < x < 39.

Note that range = max - min = 39-8 = 31 which is not the range of 56 that we want. So there's no way scenario C can be possible here.

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