Question

Please answer the following questions:

Check all outliers of this data of book costs(dollars).

19 95 30 18 21 75 38 49 53 6 54 143

19 95 30 18 21 75 38 49 53 6 54 143 none

In the following data set of candy bag weights(lbs), determine the z-score of 20.

46 75 78 57 14 37 20 46 82

z-score =
	[three decimal places]

A distribution of book costs(dollars) has the following 5-number summary. What percentage of data is between 51 and 65 ?

25	51	65	93	118
Min	Q1	Median	Q3	Max

Percentage is	%
	[do no include the % sign]

Answer 1

Following is the ordered data set:

S.No.	X
1	6
2	18
3	19
4	21
5	30
6	38
7	49
8	53
9	54
10	75
11	95
12	143

Since there are 12 data values so first half of data set will have 6 data values. That is first quartile will be average of 3rd and 4th data values. So,

Since there are 12 data values so second half of data set will have 6 data values. That is third quartile will be average of 9th and 10th data values. So,

​

The inter quartile range will be

Lower fence:

Upper fence:

Since data value 143 is not between the fences -46.75 and 130.75 so it is an outlier.

Hence, the outlier is 143.

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

To find z-score first we need to find the mean and standard deviation of data. Following is the output of descriptive statistics:

The z-score for X = 20 is

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

Since 51 is first quartile and 65 is median so 25% data values lie between 51 and 65.

Hence, required percentage is 25%.