Question

A random sample of 20 college professors is selected from all professors at a university. The following list gives their ages: 27, 52, 49, 63, 60, 57, 48, 53, 47, 42, 51, 54, 62, 60, 49, 58, 56, 47, 44, 49 [a] (1 point) What is the POPULATION in this problem? [b] (1 point) What is the SAMPLE? [c] (1 point) State whether the ages of professors are QUANTITATIVE or QUALITATIVE? [d] (1 point) If quantitative, is it DISCRETE or CONTINUOUS? [e] (6 points) Using the age sample data above, find the mean. median, mode, range. standard deviation and variance. Be sure to include the units in your answers. You do not need to show work. Round to 1 decimal place. [f] (2 points) Find the inter-quartile range of the age sample data. Show work. [g] (4 points) Find the "fences". Then use the fences to determine whether there are any outliers. Show all work. [h] (4 points) Draw a boxplot. Draw a boxplot. (Label the 5 number summary. Be sure to include outlier(s) if any.)

Answer 1

Here in this scenario the Statistical survey is calculated in a university to know the age of college professors at University.

Here A random sample of 20 college professors is selected from all professors at a university. The following list gives their ages: 27, 52, 49, 63, 60, 57, 48, 53, 47, 42, 51, 54, 62, 60, 49, 58, 56, 47, 44, 49 .

a) in this scenario the all professors at a university is a population intrest ​​​​​​. Because we have to select our sample from the all professors at University which is our sample.

b) similarly as above i said the all professors at University is population intrest and 20 professors selected from all professors at University is our sample.

c) here we collect the age of 20 professors and obviously it is quantitative data which in number.

d) from the above we collected the ages of professors and here note that the age is continuous data. It is not discrete.

e) from the given sample age we have to find out the mean median mode, sample Standerd deviation and variance as below,

Mean X bar = sum of all obs. / no. of obs.

= 1028/20

Mean Xbar = 51.4

Median to find out the median we have to arrange the data in ascending order as below,

27,42,44,47,47,48,49,49,49,51,52,53,54,56,57,58,60,60,62,63

Median = 51+52/2

Median = 51.5

Now, Mode

Mode is the most frequent value in dataset,

The most frequent value is 49 which is occure 3 times.

So mode = 49.

The sample Standerd deviation and sample variance is computed as below,

The sample Standerd deviation is 8.3 and sample variance is 68.8 (rounded to one decimal places).

f) to find out inter Quartile Range we need 1st and 3rd quartiles and it is computed as below,

We need to compute the first quartile (Q_1Q1​) based on the data provided.

Position	X (Asc. Order)
1	27
2	42
3	44
4	47
5	47
6	48
7	49
8	49
9	49
10	51
11	52
12	53
13	54
14	56
15	57
16	58
17	60
18	60
19	62
20	63

The next step is to compute the position (or rank) of the first quartile. The following is obtained:

the first Quartile is 47.25

Similarly Q3 is,

the third Quartile Q3 is 57.75 .

The inter Quartile Range Q3-Q1 is 57.75-47.25

IQR = 10.5.

The inter Quartile Range is 10.5.

g) the lower and upper fence is calculated using following formula,

LF = Q1 - 1.5 * IQR
UF = Q3 + 1.5 * IQR

Lower fence: 32.5
Upper fence: 72.5

h ) now the boxplot is constructed as below,

Sample size: 20
Median: 51.5
Minimum: 27
Maximum: 63
First quartile: 47.25
Third quartile: 57.75
Interquartile Range: 10.5
Outlier: 27

There is one outlier in data the outlier is 27.

This is answer of all sub Questions.

Thank you.