Question

Frequency Table

Number of Years	Frequency		Number of Years	Frequency
7	1		22	1
14	3		23	1
15	1		26	1
18	1		40	2
19	4		42	2
20	3

Give the 5-number summary of these data

Using the answer from question a), make a box plot of these data. Make sure to use a numbered axis.

Using a value width of 10, starting from 0 (e.g. 0 – 10), make a histogram of these data. Label your axes.

What is the interquartile range?

Are there any outliers?

Please show work

Answer 1

solution:

Let's write the given data in data set

[ 7 , 14 , 14 , 14 , 15 , 18 , 19 , 19 , 19 , 19 , 20 , 20 , 20 , 22, 23 , 26 , 40 , 40 , 42 , 42 ]

Total No.of observations (n) = 20

a) Here, Range = Max - Min = 42 - 7 = 35

No.of possible classes = = =~ 4

Therefore,Class width = Range / No.of classes = 35/4 =~ 9

But consider class width = 10 [since,given ]

Frequency table:

No.of years	Frequency
0 -10	1
10 - 20	9
20 - 30	6
30 -40	0
40 - 50	4

Histogram:

b)

Here, First Quartile (Q1) = 0.25*(n+1) th term

= 0.25*21 th term

= 5.25 th term

= Average of 5th and 6 th term [ From Acending order list]

= (15+18) / 2

= 16.5

Second Quartile (or) Median = Average of (n/2)th and (n/2)+1th term [since,n is even ]

= Average of 10th and 11th term

= (19+20) / 2

= 19.5

Here, Third Quartile (Q3) = 0.75*(n+1) th term

= 0.75*21 th term

= 15.75 th term

= Average of 15th and 16 th term [ From Acending order list]

= (23 + 26) / 2

= 24.5

Here, Minimum = 7 and Maximum = 42

i) Five numbered summary:

  1)Minimum value = 7 2) First Quartile(Q1) = 16.5 3) Median = 19.5 4) Third Quartile(Q3) = 24.5

5) Maximum value = 42

ii) Inter Quartile Range(IQR)

  Inter Quartile Range(IQR) = Q3 - Q1 = 24.5 - 16.5 = 8

iii) Outliers:

Outliers are present outside the range of : Q1 - 1.5 *(IQR) - Q3 +1.5 *(IQR)

: 16.5 - 12 - 24.5 + 12

: 4.5 - 36.5

Therefore, Outliers are: 40 , 40 , 42 , 42

Boxplot for given data is :

we can also Represent the boxplot with outliers in Boxplot as follows