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Elza [17]
2 years ago
6

Use the data given below to answer the following questions 68,63,67,66,65,87,69,61,86,82,28, a. What is the outlier of the data?

Explain why you consider this number the outlier b.Calculate the mean of the given data set.You must show your work to receive all possible points.c. Calculate the mean of the given data set excluding the outlier value. You must show your work to receive all possible points
Mathematics
2 answers:
AnnyKZ [126]2 years ago
7 0

Answer:

A)28

B)67.45

C)71.4  

Step-by-step explanation:

We are given the following data:

68,63,67,66,65,87,69,61,86,82,28

a) The outlier in the data is 28 as we can clearly see all the data points in the given data set ranges from 60 to 88 but their is a single entry of 28 which is different.

b) Mean = \frac{\text{Sum of all observations}}{\text{Total number of observations}}\\\\ = \frac{68+63+67+66+65+87+69+61+86+82+28}{11}\\\\=\frac{742}{11} = 67.45

c)Mean = \frac{\text{Sum of all observations}}{\text{Total number of observations}}\\\\ = \frac{68+63+67+66+65+87+69+61+86+82}{10}\\\\=\frac{714}{10} = 71.4

Lady_Fox [76]2 years ago
3 0
The outlier is 28 because there is a big gap between 28 and 61

to find the mean add all the numbers together then
divide the number of values added
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erma4kov [3.2K]

Answer:

a) s = 8.81

b) Q1 = 43.4, Q2 = 49.4, Q3 = 57.35

c) See below

Step-by-step explanation:

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In order to find the standard deviation, we need the mean first. The mean is defined as

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s=\sqrt{\displaystyle\frac{\displaystyle\sum_{i=1}^n(x_i-\bar x)^2}{n-1}}

and we have that our standard deviation is

s = 8.81

(b) Find the quartiles of the reflectance for these smolts

To find the quartiles, we must sort the data from lowest to largest:  

33.6,  37.7,  38.3,  38.7,  42,  42,  42.2,  42.4,  42.7,  42.8,  42.9,  43.1,  43.7,  43.8,  44.2,  44.6,  45.5,  45.7,  46.3,  46.6,  47.4,  47.6,  47.7,  47.9,  49.2,  49.6,  50.5,  50.9,  51.3,  53,  53.9,  54.8,  54.9,  55.5,  56,  56,  56.2,  57.1,  57.6,  58.3,  59,  59.5,  60.4,  63.2,  63.4,  63.5,  64.6,  68,  69.1,  69.2

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So the 1st quartile is

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Q_2=\displaystyle\frac{49.2+49.6}{2}=49.4

The 3rd quartile is the point between the 38th and 39th data (so 75% of the data are below it and 25% above it)

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(c) Do you prefer the standard deviation or the quartiles as a measure of spread for these data? Give reasons for your preference.

In this case, we prefer the quartiles as a measure of spread since the data are very scattered around the mean and there is no a central tendency.

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