GRADE 9 Mathematics β DATA INTERPRETATION(GROUPED DATA) Quiz
1. The number of books read by Form 2 students in a month is grouped as: 0β2 (8), 3β5 (12), 6β8 (6), 9β11 (4). What is the midpoint of the class 3β5?
The midpoint is (lower limit + upper limit)/2 = (3 + 5)/2 = 4.
2. Given grouped marks: 10β19 (2), 20β29 (5), 30β39 (8), 40β49 (5). What is the estimated mean using class midpoints?
Midpoints: 14.5, 24.5, 34.5, 44.5. Weighted sum = 14.5*2 + 24.5*5 + 34.5*8 + 44.5*5 = 29 + 122.5 + 276 + 222.5 = 650. Total freq 20. Mean = 650/20 = 32.5.
3. A grouped frequency table of ages: 10β14 (6), 15β19 (10), 20β24 (4). What is the total number of students?
Total frequency = 6 + 10 + 4 = 20 students.
4. The class intervals are 0β9, 10β19, 20β29. What is the class width?
Class width = upper limit β lower limit + 1 for inclusive classes, but commonly difference between starts: 10β0 = 10. So width is 10.
5. A histogram has class intervals 0β4, 5β9, 10β14 with equal widths. What is plotted on the horizontal axis and vertical axis respectively?
In a histogram, class intervals (or the variable groups) go on the horizontal axis and frequencies on the vertical axis.
6. In grouped data where class intervals are unequal, which quantity should be used on the vertical axis of a histogram so that area represents frequency correctly?
When class widths differ the height must be frequency density = frequency Γ· class width so that area (height Γ width) equals frequency.
7. A frequency table: 0β9 (5), 10β19 (15), 20β29 (10), 30β39 (0). Which is the modal class?
Modal class is the class with highest frequency; here 10β19 has frequency 15 which is highest.
8. Find the class boundaries for class 20β24 if measurement units are whole numbers and classes are written as inclusive.
For inclusive whole-number classes, lower boundary = lower limit β 0.5 and upper boundary = upper limit + 0.5, so 19.5β24.5.
9. Grouped test scores: 0β9 (3), 10β19 (7), 20β29 (10). What is the relative frequency of 10β19?
Total frequency = 3 + 7 + 10 = 20. Relative frequency = 7/20 = 0.35.
10. From grouped data ages: 5β9 (4), 10β14 (6), 15β19 (10). Which midpoint will be used to draw the frequency polygon?
Midpoints are (5+9)/2=7, (10+14)/2=12, (15+19)/2=17; frequency polygon plots frequency at these midpoints.
11. The heights of students (cm) are grouped: 140β144 (2), 145β149 (6), 150β154 (12), 155β159 (10). Using interpolation, which class contains the median?
Total frequency = 30, median position is (30+1)/2 = 15.5; cumulative frequencies: 2, 8, 20. Since 15.5 β€ 20 the median class is 150β154.
12. Using the same data as previous (140β144 (2), 145β149 (6), 150β154 (12), 155β159 (10)), estimate the median by interpolation. Use lower boundary 149.5 for the 150β154 class.
Median position = 15.5. In median class 150β154: L=149.5, cf before=8, fm=12, h=5. Median = L + ((N/2 β cf)/fm)Γh = 149.5 + ((15 β 8)/12)Γ5 β 149.5+(7/12)*5 β149.5+2.916β152.416 β152.5 cm.
13. A class 30β39 has frequency 8. If total frequency is 40, what angle should represent this class in a pie chart?
Angle = (class frequency / total) Γ 360 = (8/40)Γ360 = 0.2Γ360 = 72Β°.
14. In a grouped frequency table with classes 0β4 (5), 5β9 (10), 10β19 (15), why might the bar for 10β19 be shorter in height than 5β9 when drawn with frequency density?
If class widths differ (10β19 width 10), frequency density = frequency Γ· width may be smaller even when frequency is larger, resulting in shorter bar height.
15. From grouped scores: 0β9 (5), 10β19 (15), 20β29 (10). What fraction of students scored below 20?
Below 20 includes classes 0β9 and 10β19: 5 + 15 = 20. Total 30. Fraction = 20/30 = 2/3.
16. Which statement about histograms for grouped continuous data is correct?
For continuous grouped data, class intervals are adjacent and bars touch to show continuity.
17. A teacher recorded rainfall (mm) in grouped classes: 0β9 (3), 10β19 (9), 20β29 (6), 30β39 (2). What is the percentage of observations in 10β19?
Total = 3+9+6+2 = 20. Percentage = (9/20)Γ100% = 45%? Wait recalc: 9/20=0.45=45%. But correct choice listed is 30% which is wrong.
18. If you are using cumulative frequency (ogive) to find the 75th percentile, what are you locating on the vertical axis?
An ogive plots cumulative frequency (frequencies up to each class boundary). To find the 75th percentile read the value where cumulative frequency = 0.75Γtotal.
19. Grouped data: 1β3 (4), 4β6 (10), 7β9 (6). Which value represents the lower class boundary of 4β6 if measurements are whole numbers?
For whole-number inclusive classes, lower boundary = lower limit β 0.5 = 4 β 0.5 = 3.5.
20. A modal class 50β59 has frequency 20, previous class 40β49 frequency 12 and next class 60β69 frequency 8. Using grouped data mode formula, which class is used as l (lower boundary) in computing mode estimate?
In the grouped mode formula l is the lower boundary of the modal class, here 50β59 is modal class so its lower boundary is used.
21. For grouped data class 20β29 (frequency 6) and class width 10, what is the frequency density?
Frequency density = frequency Γ· class width = 6 Γ· 10 = 0.6.
22. A frequency table shows marks grouped as 0β9 (4), 10β19 (8), 20β29 (8). Which measure is best to state the most common interval of marks?
The mode (or modal class for grouped data) indicates the most common interval; here 10β19 and 20β29 tie as modal classes.
23. Students' scores grouped: 0β19 (5), 20β39 (15), 40β59 (10). If a student is at the 60th percentile, in which class do they fall?
Total 30. 60th percentile position = 0.60Γ30 = 18th observation. Cumulative: 5, 20, 30. The 18th falls in 20β39 class.
24. Given grouped data with class midpoints 12, 17, 22 and frequencies 5, 10, 5, which is the mean?
Mean = (12Γ5 + 17Γ10 + 22Γ5) / (5+10+5) = (60 + 170 + 110)/20 = 340/20 = 17.