This Question is incomplete
Complete Question:
The data represents the number of runs allowed by 8 college softball pitchers. {18, 49, 38, 41, 33, 44, 42, 22}
What is the five number summary:
a) Minimum
b) Q₁
c) Median
d) Q₃
e) Maximum
Answer:
a) Minimum = 18
b) Q₁ = 27.5
c) Median = 39.5
d) Q₃ = 43
e) Maximum = 49
Step-by-step explanation:
From the above diagram, we were given the following set of data.
{18, 49, 38, 41, 33, 44, 42, 22}
Before answering any of the questions, we have to rearrange the data from the lowest to the highest (ascending order). Hence, we have:
{18, 22, 33, 38, 41, 42, 44, 49}
a) Minimum
{18, 22, 33, 38, 41, 42, 44, 49}
Looking at this set of arranged data, the minimum number is the least or lowest number.
This number is 18
b) Q₁
{18, 22, 33, 38, 41, 42, 44, 49}
Q₁ means First Quartile. The formula is = ¼(n + 1)th value
n = Number of terms in the data set = 8
= ¼(8 + 1)th value
= ¼(9)th value
= 2 1/4 value
= 2.25 value
In the above Question, the 2.25 value is the value between the second and third number.
Hence:
22+33/2 = 55/2 = 27.5
Therefore, Q₁ = 27.5
c) Median
{18, 22, 33, 38, 41, 42, 44, 49}
The median of the number is the number in the middle
For this data, we have 8 number, Hence the median is the sum of the 4th and 5th term divided by 2
4th term = 38
5th term = 41
= 38 + 41/ 2 = 79/2
= 39.5
Hence, the median = 39.5
d) Q₃
{18, 22, 33, 38, 41, 42, 44, 49}
Q₃ means Third Quartile. The formula is = ¾(n + 1)th value
n = Number of terms in the data set = 8
= ¾(8 + 1)th value
= ¾(9)th value
= 6 3/4 value
= 6.75 value
In the above Question, the 6.75 value is the value between the sixth and seventh number.
Hence:
42+44/2 = 86/2 = 43
Therefore, Q₃ = 43
e) Maximum
{18, 22, 33, 38, 41, 42, 44, 49}
Looking at this set of arranged data, the Maximum number is the highest number.
This number is 49
/6 (when finding the inverse, always take the positive value, ignore the negative sign)