FREE Statistics Worksheets Year 4 - Free Printable
Educational worksheet: FREE Statistics Worksheets Year 4. Download and print for classroom or home learning activities.
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Step-by-step solution for: FREE Statistics Worksheets Year 4
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Show Answer Key & Explanations
Step-by-step solution for: FREE Statistics Worksheets Year 4
Here are the step-by-step solutions for each question on the worksheet.
(1) Probability of drawing a Queen
* Step 1: A standard deck of cards has 52 cards in total.
* Step 2: There are 4 suits (Hearts, Diamonds, Clubs, Spades), and each suit has one Queen. So, there are 4 Queens in total.
* Step 3: The probability is the number of favorable outcomes (Queens) divided by the total number of outcomes (total cards).
* Calculation: $4 / 52$. This fraction can be simplified by dividing both numbers by 4.
* Result: $1 / 13$.
(2) Probability of drawing a red King
* Step 1: The total number of cards is still 52.
* Step 2: We need to find how many Kings are red. The red suits are Hearts and Diamonds. There is one King of Hearts and one King of Diamonds. So, there are 2 red Kings.
* Step 3: Calculate the probability: 2 red Kings divided by 52 total cards.
* Calculation: $2 / 52$. Simplify by dividing by 2.
* Result: $1 / 26$.
(3) Average of 6 subjects
* Step 1: Find the total marks for the first 5 subjects. The average is 86, so multiply the average by the number of subjects: $86 \times 5 = 430$.
* Step 2: Add the mark for the 6th subject (80) to this total: $430 + 80 = 510$.
* Step 3: Divide the new total by the new number of subjects (6) to find the new average.
* Calculation: $510 / 6 = 85$.
(4) Average of five-digit numbers
* Step 1: The digits are 2, 1, 8, 7, and 6.
* Step 2: Instead of listing every single number, we can look at the place values. In any position (ones, tens, hundreds, etc.), each digit will appear an equal number of times across all possible combinations.
* Step 3: First, find the average of the digits themselves: $(2 + 1 + 8 + 7 + 6) / 5 = 24 / 5 = 4.8$.
* Step 4: Because the digits are distributed evenly across all positions, the average of all the formed numbers will simply be the number made of this average digit repeated for each place value.
* Calculation: The average number is $4.8 \times 11,111$ (or simply writing 4.8 five times as 44,444.4). Let's verify with the sum method.
* Sum of digits = 24.
* Total permutations = $5! = 120$.
* Each digit appears in each column $120 / 5 = 24$ times.
* Sum for one column = $24 \times 24 = 576$.
* Total Sum = $576 \times (10,000 + 1,000 + 100 + 10 + 1) = 576 \times 11,111 = 6,399,936$.
* Average = $6,399,936 / 120 = 53,332.8$.
* *Correction*: My shortcut in Step 4 was slightly off because the average digit is 4.8, not an integer. Let's stick to the rigorous calculation:
* Average = (Sum of digits / Count of digits) $\times$ 11,111
* Average = $4.8 \times 11,111 = 53,332.8$.
(5) Median of the set
* Step 1: List the numbers: 18, 17, 17, 15, 13, 17, 10, 19, 15, 21, 19.
* Step 2: Order them from smallest to largest:
10, 13, 15, 15, 17, 17, 17, 18, 19, 19, 21.
* Step 3: Count the numbers. There are 11 numbers.
* Step 4: The median is the middle number. For 11 numbers, the middle is the 6th number.
* Result: The 6th number is 17.
(6) Probability of brown eyes
* Step 1: Find the total number of students by adding the counts for each eye color: $11 + 10 + 11 + 11 + 3 = 46$.
* Step 2: Identify the number of students with brown eyes: 11.
* Step 3: The probability is the number of brown-eyed students divided by the total number of students.
* Result: $11 / 46$.
(7) Probability of hitting the shaded part
* Step 1: Count the total number of equal sections in the circle. There are 12 sections.
* Step 2: Count the number of shaded sections. There are 5 shaded sections.
* Step 3: The probability is the shaded sections divided by the total sections.
* Result: $5 / 12$.
(8) Weight of the new person
* Step 1: Find the total weight of the original 5 people. Multiply the average (75.7) by the number of people (5): $75.7 \times 5 = 378.5$ kg.
* Step 2: When the new person arrives, there are now 6 people. The new average is 76.5 kg.
* Step 3: Find the total weight of all 6 people: $76.5 \times 6 = 459$ kg.
* Step 4: Subtract the original total weight from the new total weight to find the weight of just the new person.
* Calculation: $459 - 378.5 = 80.5$ kg.
Final Answer:
(1) 1/13
(2) 1/26
(3) 85
(4) 53,332.8
(5) 17
(6) 11/46
(7) 5/12
(8) 80.5 kg
(1) Probability of drawing a Queen
* Step 1: A standard deck of cards has 52 cards in total.
* Step 2: There are 4 suits (Hearts, Diamonds, Clubs, Spades), and each suit has one Queen. So, there are 4 Queens in total.
* Step 3: The probability is the number of favorable outcomes (Queens) divided by the total number of outcomes (total cards).
* Calculation: $4 / 52$. This fraction can be simplified by dividing both numbers by 4.
* Result: $1 / 13$.
(2) Probability of drawing a red King
* Step 1: The total number of cards is still 52.
* Step 2: We need to find how many Kings are red. The red suits are Hearts and Diamonds. There is one King of Hearts and one King of Diamonds. So, there are 2 red Kings.
* Step 3: Calculate the probability: 2 red Kings divided by 52 total cards.
* Calculation: $2 / 52$. Simplify by dividing by 2.
* Result: $1 / 26$.
(3) Average of 6 subjects
* Step 1: Find the total marks for the first 5 subjects. The average is 86, so multiply the average by the number of subjects: $86 \times 5 = 430$.
* Step 2: Add the mark for the 6th subject (80) to this total: $430 + 80 = 510$.
* Step 3: Divide the new total by the new number of subjects (6) to find the new average.
* Calculation: $510 / 6 = 85$.
(4) Average of five-digit numbers
* Step 1: The digits are 2, 1, 8, 7, and 6.
* Step 2: Instead of listing every single number, we can look at the place values. In any position (ones, tens, hundreds, etc.), each digit will appear an equal number of times across all possible combinations.
* Step 3: First, find the average of the digits themselves: $(2 + 1 + 8 + 7 + 6) / 5 = 24 / 5 = 4.8$.
* Step 4: Because the digits are distributed evenly across all positions, the average of all the formed numbers will simply be the number made of this average digit repeated for each place value.
* Calculation: The average number is $4.8 \times 11,111$ (or simply writing 4.8 five times as 44,444.4). Let's verify with the sum method.
* Sum of digits = 24.
* Total permutations = $5! = 120$.
* Each digit appears in each column $120 / 5 = 24$ times.
* Sum for one column = $24 \times 24 = 576$.
* Total Sum = $576 \times (10,000 + 1,000 + 100 + 10 + 1) = 576 \times 11,111 = 6,399,936$.
* Average = $6,399,936 / 120 = 53,332.8$.
* *Correction*: My shortcut in Step 4 was slightly off because the average digit is 4.8, not an integer. Let's stick to the rigorous calculation:
* Average = (Sum of digits / Count of digits) $\times$ 11,111
* Average = $4.8 \times 11,111 = 53,332.8$.
(5) Median of the set
* Step 1: List the numbers: 18, 17, 17, 15, 13, 17, 10, 19, 15, 21, 19.
* Step 2: Order them from smallest to largest:
10, 13, 15, 15, 17, 17, 17, 18, 19, 19, 21.
* Step 3: Count the numbers. There are 11 numbers.
* Step 4: The median is the middle number. For 11 numbers, the middle is the 6th number.
* Result: The 6th number is 17.
(6) Probability of brown eyes
* Step 1: Find the total number of students by adding the counts for each eye color: $11 + 10 + 11 + 11 + 3 = 46$.
* Step 2: Identify the number of students with brown eyes: 11.
* Step 3: The probability is the number of brown-eyed students divided by the total number of students.
* Result: $11 / 46$.
(7) Probability of hitting the shaded part
* Step 1: Count the total number of equal sections in the circle. There are 12 sections.
* Step 2: Count the number of shaded sections. There are 5 shaded sections.
* Step 3: The probability is the shaded sections divided by the total sections.
* Result: $5 / 12$.
(8) Weight of the new person
* Step 1: Find the total weight of the original 5 people. Multiply the average (75.7) by the number of people (5): $75.7 \times 5 = 378.5$ kg.
* Step 2: When the new person arrives, there are now 6 people. The new average is 76.5 kg.
* Step 3: Find the total weight of all 6 people: $76.5 \times 6 = 459$ kg.
* Step 4: Subtract the original total weight from the new total weight to find the weight of just the new person.
* Calculation: $459 - 378.5 = 80.5$ kg.
Final Answer:
(1) 1/13
(2) 1/26
(3) 85
(4) 53,332.8
(5) 17
(6) 11/46
(7) 5/12
(8) 80.5 kg
Parent Tip: Review the logic above to help your child master the concept of stats worksheets.
