1Two cricket players scored these runs in their last eleven matches. Player A: 21, 25, 71, 5, 42, 15, 85, 64, 110, 32, 35. Player B: 12, 55, 101, 34, 60, 41, 72, 6, 22, 7, 18. Find the lowest value, first quartile, median, third quartile and highest value of both data sets.
2Show the scores of Player A and Player B as separate whisker box plots on graph paper.
3On the basis of the box plots, compare the scores of Player A and Player B using the median and the interquartile range.
4The battery life, in hours, of two mobile brands, Brand A and Brand B, is shown in the chart comparing smartphone battery life. On the basis of the median, which brand's battery generally lasts longer? Choose from: Brand A, Brand B, both are equal, neither.
5In the same smartphone battery chart, which brand's battery life is more consistent? Choose from: Brand B because its range is large; Brand A because its box (interquartile range) is small and all its values are close together; both brands are equally reliable; Brand B because it gives battery backup up to 38 hours.
6In the same smartphone battery chart, which brand is more certain to give at least a fairly long battery life? Choose from: Brand B (15 hours), Brand A (20 hours), the least time is the same for both, cannot be said.
7What does the red line (the thick line inside each box) of the smartphone battery chart show? Choose from: the highest battery life, the lowest battery life, the middle battery life (where 50% of the values lie on each side), the price of the battery.
8The rice yield in kilograms over ten years with two fertilizers, A and B, is shown in the rice yield box plots. With which fertilizer does a minimum rice harvest look more certain?
9If you were a farmer and wanted to take less risk, which fertilizer would you choose and why? (Hint: look at the IQR.)
10Is there any year in which Fertilizer B gave an unusually large harvest? How does the plot show it?
11The box plots comparing Battery A and Battery B show battery life in hours. What is the median battery life of Battery A?
12In the same chart, what is the median battery life of Battery B?
13Find the range of the battery life of both Battery A and Battery B.
14Which battery would you buy? Support your decision with reasons.
15The numbers of mobiles sold in one week by two shops are: Shop A: 8, 5, 14, 9, 11, 7, 18 and Shop B: 10, 12, 8, 16, 6, 3, 2. Find the lowest value, first quartile, median, third quartile and highest value of both data sets.
16Show the mobile sales of the two shops as separate whisker box plots on graph paper.
17Compare the numbers of mobiles sold by the two shops on the basis of the median and the interquartile range.
18The marks of students in an examination are: 20-30: 4, 30-40: 6, 40-50: 10, 50-60: 17, 60-70: 11, 70-80: 9, 80-90: 3. Write the relation between the quartile deviation, the first quartile and the third quartile.
19For the marks 20-30: 4, 30-40: 6, 40-50: 10, 50-60: 17, 60-70: 11, 70-80: 9, 80-90: 3, find the standard deviation.
20For the same marks, find the coefficient of variation.
21The marks of 40 students in the second terminal mathematics examination are: 20-30: 5, 30-40: 9, 40-50: 12, 50-60: 7, 60-70: 4, 70-80: 3. Write the formula for finding the mean deviation from the mean.
22For the marks 20-30: 5, 30-40: 9, 40-50: 12, 50-60: 7, 60-70: 4, 70-80: 3, find the standard deviation.
23If the standard deviation of the marks in the first terminal examination was 8.75, compare the marks of the first and second terminal examinations.
24The monthly salaries of 50 bank employees are: more than Rs 20000: 50, more than 30000: 45, more than 40000: 25, more than 50000: 9, more than 60000: 4, more than 70000: 2. What is quartile deviation?
25For the salary data above, which measure of dispersion is suitable? Give a reason.
26From the salary data, find the quartile deviation and its coefficient.
27The mathematics marks of 40 students are: 75, 35, 45, 47, 60, 61, 56, 39, 56, 52, 42, 60, 69, 42, 43, 46, 55, 56, 35, 51, 58, 61, 49, 57, 51, 59, 47, 52, 57, 55, 48, 58, 54, 67, 46, 56, 39, 48, 51, 60. Write the formula for calculating the coefficient of variation.
28Present the 40 marks above in a frequency table with class interval 5.
29Calculate the coefficient of variation of the 40 marks.
30In analysing the results of two students A and B, the coefficients of variation were found to be 21% for A and 12% for B. Whose result is more uniform? Give a reason.
31The marks of 60 students of a school are: Mathematics 30-40: 5, 40-50: 11, 50-60: 16, 60-70: 12, 70-80: 10, 80-90: 4, 90-100: 2; Science 30-40: 4, 40-50: 8, 50-60: 16, 60-70: 20, 70-80: 6, 80-90: 4, 90-100: 2. Find the lowest value, first quartile, median, third quartile and highest value of both subjects.
32Find the quartile deviation and its coefficient for the mathematics and science marks.
33In which subject are the marks more uniform? Give a reason.
34Draw separate whisker box plots of the mathematics and science marks on graph paper.
35Why must two box plots be drawn on the same scale before they are compared?
36Two classes took the same test. Class X: median 62, interquartile range 10. Class Y: median 58, interquartile range 25. Compare the two classes.
37The ages of students in a box plot are: lowest 10 years, Q1 11 years, median 13 years, Q3 16 years, highest 18 years. Find the interquartile range and the range.