Introduction to Practice Set Solutions
A set of elements or information or numbers are referred as data set. Data set can hold any types of data. Data can be represented as tables and graphs. In tables data are stored as rows and columns. Data sets are classified into sequential data set and partitioned data set. In sequential data set data are stored as consecutively. In partitioned data set store the address, so that it is possible to access the data easily. Let us practice the data set solutions in statistics.
Practice Statistics Data Set Solutions - Example
Ex: Find the mean, median, mode, and range for the data set: {20, 27, 15, 16, 42, 28, 20}.
Solution:First arrange the set in ascending order {15, 16, 20, 20, 27, 28, 42}
Mean:Mean or average is the sum of all the elements in the set divided by total number of elements in a set.
Mean = Sum of elements in a set / Number of elements in a set
= {15, 16, 20, 20, 27, 28, 42}/ 7
= `168/7` = 24
Therefore mean is 24
Median:Median is the middle value of the data set after the arrangement of ascending or descending order the data set.
Therefore median is 20.
Mode:If any of the value in data set is repeated two or more times then that is referred to as mode.
20 is repeated twice.
Hence, the mode of the given data set is 20.
Range:Difference between the maximum and minimum value of the data set is called the range.
Range = Maximum value – Minimum value
= 42 – 15
= 27
Therefore range is 27.
Practice Probability Data Set Solutions - Example
Example: When a pair of balanced dice is rolled, and what are the probabilities of getting the sum (1) 12 (2) 12 or 11 (3) 11or 10. Find the solutions.
Solution:-The sample space S = {(1, 1), (1, 2) … (6, 6)}
Number of possible outcomes n(S) = 36
Let A be the event of getting sum 12, B be the event of getting the sum 11
and C be the event of getting sum 10.
A = {(6, 6)} n(A) = 1.
B = {(5, 6), (6, 5) n(B) = 2
C = {(4, 6), (5, 5), (6, 4)}n(C) = 3
(1) P (getting sum 12) = P(A) =`(n(A))/(n(S)) = 1/36`
P(12) = `1/36`
(2) P(12 or 11) = P(A or B) = P(A ∪ B)
= P(A) + P(B) (A and B are mutually exclusive i.e. A∩B=φ)
= `1/36 + 2/36 = 3/36= 1/12`
P (12 or 11) = `1/12`
(3) P(11 or 10) = P(B or C) solving the above the problems also.
= P(B) + P(C) (B and C are mutually exclusive)
= `2/36 + 3/36 = 5/36`
P (11 or 10) = `5/36`
Data Set Solutions – Practice Problems
Solve these practice problems
Practice 1: Find the mean, median, mode, and range for the data set: {25, 32, 20, 21, 47, 33, 25}.
Ans: Mean – 29, Median – 25, Mode – 25, Range – 27
Practice 2: When a pair of balanced dice is rolled, and what are the probabilities of getting the sum (1) 10 (2) 10 or 9 (3) 9 or 8.
Ans: (1) `1/12` , (2) `7/36` , (3) `1/4`
A set of elements or information or numbers are referred as data set. Data set can hold any types of data. Data can be represented as tables and graphs. In tables data are stored as rows and columns. Data sets are classified into sequential data set and partitioned data set. In sequential data set data are stored as consecutively. In partitioned data set store the address, so that it is possible to access the data easily. Let us practice the data set solutions in statistics.
Practice Statistics Data Set Solutions - Example
Ex: Find the mean, median, mode, and range for the data set: {20, 27, 15, 16, 42, 28, 20}.
Solution:First arrange the set in ascending order {15, 16, 20, 20, 27, 28, 42}
Mean:Mean or average is the sum of all the elements in the set divided by total number of elements in a set.
Mean = Sum of elements in a set / Number of elements in a set
= {15, 16, 20, 20, 27, 28, 42}/ 7
= `168/7` = 24
Therefore mean is 24
Median:Median is the middle value of the data set after the arrangement of ascending or descending order the data set.
Therefore median is 20.
Mode:If any of the value in data set is repeated two or more times then that is referred to as mode.
20 is repeated twice.
Hence, the mode of the given data set is 20.
Range:Difference between the maximum and minimum value of the data set is called the range.
Range = Maximum value – Minimum value
= 42 – 15
= 27
Therefore range is 27.
Practice Probability Data Set Solutions - Example
Example: When a pair of balanced dice is rolled, and what are the probabilities of getting the sum (1) 12 (2) 12 or 11 (3) 11or 10. Find the solutions.
Solution:-The sample space S = {(1, 1), (1, 2) … (6, 6)}
Number of possible outcomes n(S) = 36
Let A be the event of getting sum 12, B be the event of getting the sum 11
and C be the event of getting sum 10.
A = {(6, 6)} n(A) = 1.
B = {(5, 6), (6, 5) n(B) = 2
C = {(4, 6), (5, 5), (6, 4)}n(C) = 3
(1) P (getting sum 12) = P(A) =`(n(A))/(n(S)) = 1/36`
P(12) = `1/36`
(2) P(12 or 11) = P(A or B) = P(A ∪ B)
= P(A) + P(B) (A and B are mutually exclusive i.e. A∩B=φ)
= `1/36 + 2/36 = 3/36= 1/12`
P (12 or 11) = `1/12`
(3) P(11 or 10) = P(B or C) solving the above the problems also.
= P(B) + P(C) (B and C are mutually exclusive)
= `2/36 + 3/36 = 5/36`
P (11 or 10) = `5/36`
Data Set Solutions – Practice Problems
Solve these practice problems
Practice 1: Find the mean, median, mode, and range for the data set: {25, 32, 20, 21, 47, 33, 25}.
Ans: Mean – 29, Median – 25, Mode – 25, Range – 27
Practice 2: When a pair of balanced dice is rolled, and what are the probabilities of getting the sum (1) 10 (2) 10 or 9 (3) 9 or 8.
Ans: (1) `1/12` , (2) `7/36` , (3) `1/4`
