4.1 Statistics

Topic	4.1 Statistics
Tag	Statistics; Variable; Mean; Median; Mode; Interquartile range; Descriptive; Variance; Standard deviation; Correlation; Data; Cumulative frequency; Line of best fit; Regression
Source	M16-TZ1-P1-2(HL)
Question Text	The mean score of the first three basketball players is 127 points. The score for the fourth player is then recorded and the mean score of the first four players is 140 seconds. Find the score achieved by the fourth player.
Total Mark	4
Correct Answer	179
Explanation	n/a
Mark Scheme	Step 1: Consider the given information. In this case, we are given the mean score of the first 3 players. Using the information, we can calculate the total score of those players. total score of first 3 players = $127 \times 3 = 381$ Then, we can calculate the total score of the first 4 players using the mean score for the first 4 players. total score of first 4 players = $140\times4 = 560$ Step 2: Combine the given information. We can find the score achieved by the 4th player by subtracting the total score of the first 3 players from the total score of the first 4 players. 4th player score = $560 - 381 = 179$ (points)

Topic	4.1 Statistics
Tag	Statistics; Variable; Mean; Median; Mode; Interquartile range; Descriptive; Variance; Standard deviation; Correlation; Data; Cumulative frequency; Line of best fit; Regression
Source	M15-TZ1-P1-2(HL)
Question Text	A mathematics test is given to a class of 10 students. One student scores 0, but all the other students score 100. (a) Find the mean score for the class.
Total Mark	2
Correct Answer	90
Explanation	n/a
Mark Scheme	Mean = $\frac{1 \times 0+9 \times 100}{10}=90$
Question Text	(b) Write down the median score.
Total Mark	1
Correct Answer	100
Explanation	n/a
Mark Scheme	n/a
Question Text	(c) Write down the number of students who scored. (i) Above the mean score; Total Mark: 1 Correct Answer: 9 Explanation: n/a Mark Scheme: n/a (ii) Below the median score. Total Mark: 1 Correct Answer: 1 Explanation: n/a Mark Scheme: n/a

Topic	4.1 Statistics
Tag	Statistics; Variable; Mean; Median; Mode; Interquartile range; Descriptive; Variance; Standard deviation; Correlation; Data; Cumulative frequency; Line of best fit; Regression
Source	M14/5/MATHL/HP1/ENG/TZ1/X/2
Question Text	Four numbers are such that their mean is 12, their median is 13 and their mode is 14. Find the smallest of the four numbers.
Total Mark	5
Correct Answer	8
Explanation	n/a
Mark Scheme	Sum = $12 \times 4 = 48$ As the mode is 14, two of the numbers are 14. As the median is 13, one of the number must be 12. As the sum is 48, the last number is 8

Topic	4.1 Statistics
Tag	Statistics; Variable; Mean; Median; Mode; Interquartile range; Descriptive; Variance; Standard deviation; Correlation; Data; Cumulative frequency; Line of best fit; Regression
Source	M18/5/MATHL/HP2/ENG/TZ1/XX/8
Question Text	Each of the 10 students in a class are asked how many pets they own. One student owns three pets and no students own more than three pets. The mean and variance of the number of pets owned by students in the class are 11/10 and 109/100 respectively. Find the number of students in the class who do not own a pet.
Total Mark	7
Correct Answer	4
Explanation	n/a
Mark Scheme	Let $p$ have no pets, $q$ have one pet and $r$ have two pets Use variance equation, $p+q+r+1=10 \\ 0 p+1 q+2 r+3=11$ Solve a system of linear equations, $\frac{0 p+1 q+4 r+9}{10}-\left(\frac{11}{10}\right)^2=\frac{109}{100} \\ q+4 r+9=23$ $r=3, q=2, p=4$ So 4 students have no pets.