Question

Use Statkey for the following numbers:

18 54 64 46 91 38 25 45 67 57 48 44 63

83 84 79 52 54 41 52 56 76 41 75 79 68

28 55 77 68 33 65 59 37 61 70 47 51 32

56 19 45 29 63 75 39 84 48 42 36

1. Does this data come from a "mound-shaped", distribution? Justify your answer.

2. Is the data symmetric or skewed? Justify your answer.

3. Are there any TRUE outliers, what are they, and what percent of the sample are they? Justify your answer.

4. Bell-shaped (normal) sample? why?

Answer 1

Solution:

1. Does this data come from a "mound-shaped", distribution? Justify your answer.

Solution: we check shape using the plot histogram using R software

R-Script:

x = c(18,54,64,46,91,38,25,45,67,57,48,44,63,83,84,79,52,54,41,52,56,76,41,75,79,68,28,55,77,68,33,65,59,37,61,70,47,51,32,56,19,45,29,63,75,39,84,48,42,36)
x
hist(x)

Comment : Using the above graph we say that the shape of the given data is "mound-shaped".

2. Is the data symmetric or skewed? Justify your answer.

Solution: Yes data given in the example is symmetric because 50% data lie above the median

where median is midpiont of the data. and shape of the data is like

3. Are there any TRUE outliers, what are they, and what percent of the sample are they? Justify your answer.

Solution:

R commond:

boxplot(x)

Comment:

Using this graph we say that there is no outlier for the given data because no point which is lie outside the line.

4. Bell-shaped (normal) sample? why

Solution : Yes shape  of the data is bell shape because data comes from normal distribution and 25% data lie below the Q1 and 25% data lie above the Q3 and also 50% data lies between Q3 and Q1

where Q1 is first quartile and Q3 is third Quartile

Thank You..!!

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