Sec 4 E-Math Statistical Diagrams topical questions

In a survey, 15 of 60 students chose football. Find the angle of the football sector in a pie chart.

60 people chose among three activities: 30 chose swimming, 20 running and 10 cycling. Find the three pie-chart angles and verify they total 360°.

A stem-and-leaf diagram has key 2 | 3 = 23. The rows are "2 | 3 5 8" and "3 | 0 4". List all five values.

Find the mode and the median of: 12, 15, 18, 21, 24, 24, 27.

Find the mean of 4, 7, 9, 12 and 13.

A family’s monthly expenses are shown in a pie chart in which the rent sector measures 162°. (a) What fraction of spending goes to rent? (b) If the total monthly spending is $2 400, how much is the rent?

Find the mode, the median and the range of: 3, 7, 7, 9, 12, 14, 14, 15, 18.

A histogram shows parcels by mass: 0–20 kg: 8; 20–40 kg: 15; 40–60 kg: 11; 60–80 kg: 6. (a) How many parcels were weighed? (b) State the modal class. (c) What percentage of parcels weighed more than 40 kg?

1. (a)Total parcels.[1]
2. (b)Modal class.[1]
3. (c)Percentage above 40 kg.[2]

Heights of 35 students: h ≤ 150: 4; h ≤ 160: 12; h ≤ 170: 25; h ≤ 180: 32; h ≤ 190: 35. (a) How many students have heights between 160 and 170 cm? (b) Between which two boundaries does the median height lie?

1. (a)Between 160 and 170.[2]
2. (b)Median class.[2]

A box plot has minimum 12, Q1 18, median 24, Q3 31 and maximum 40. (a) Find the interquartile range. (b) Find the range.

1. (a)IQR.[2]
2. (b)Range.[2]

A dot diagram shows the values 1, 2 and 3 with frequencies 4, 5 and 3. Find the mean, correct to 2 decimal places.

A grouped table uses classes with midpoints 5, 15 and 25 and frequencies 6, 10 and 4. Find the estimated mean of the grouped data.

A parcel depot records masses, grouped in a frequency table: 10–20 kg: 5 parcels; 20–30 kg: 9; 30–40 kg: 12; 40–50 kg: 4. (a) Find the total number of parcels. (b) State the modal class. (c) What percentage of parcels are below 30 kg, correct to 1 decimal place? (d) Explain why the table has no exact mode.

Twenty test scores are shown in a stem-and-leaf diagram with key 1 | 4 = 14: rows “1 | 4 6 8 9”, “2 | 0 5 5 5 7 8”, “3 | 1 3 5 6 6 8”, “4 | 0 2 2 4”. (a) State the mode. (b) Find the median. (c) What percentage of scores are below 25?

Delivery firms A and B report box plots. A: min 10, Q1 20, median 30, Q3 42, max 55. B: min 15, Q1 25, median 32, Q3 38, max 50. (a) Which firm has the higher median delivery time? (b) Which firm’s delivery times are more spread out? Justify using both the range and the IQR.

1. (a)Higher median.[2]
2. (b)More spread out.[3]

A shop’s 2023 sales were $40k (clothes), $50k (food) and $30k (electronics); the 2024 pie chart has exactly the same angles. A newspaper claims "sales in each category doubled". (a) Find the clothes sector angle in 2023. (b) Explain why the angles being identical does not prove the claim. (c) State what additional information would settle it.

1. (a)Clothes angle.[2]
2. (b)Why identical angles are insufficient.[2]
3. (c)What settles it.[2]

A graph shows monthly profits of $98k, $99k and $103k with the y-axis starting at $95k. (a) Explain why the graph is misleading. (b) Describe how to redraw it fairly. (c) State the honest percentage increase over the two years.

1. (a)Why misleading.[3]
2. (b)Fair redraw.[2]
3. (c)Honest increase.[1]

A cumulative frequency curve for 80 test scores gives Q1 = 22, median = 27 and Q3 = 34. (a) Find the interquartile range. (b) Estimate how many candidates scored above 34. (c) The curve reads a cumulative frequency of 55 at a score of 30. Estimate how many candidates scored 30 or less, and explain your reading.

1. (a)IQR.[2]
2. (b)Above 34.[2]
3. (c)At or below 30.[2]

Box plot P shows: minimum 12, lower quartile 20, median 26, upper quartile 34, maximum 45. Box plot Q shows: minimum 15, lower quartile 22, median 30, upper quartile 33, maximum 38. (a) Which data set has the higher median? (b) Compare the spreads of the two data sets using the IQR. (c) A candidate value of 44 joins data set P. Using the 1.5 × IQR rule, determine whether it is an outlier.

1. (a)Higher median.[2]
2. (b)Compare IQRs.[2]
3. (c)Outlier test.[2]

A pie chart of a school survey has four sectors with angles 120°, 90°, 60° and 90°. The 120° sector represents 40 students. (a) Find the total number of students surveyed. (b) Find the number of students in the 60° sector. (c) What percentage does each 90° sector represent?

1. (a)Total students.[2]
2. (b)60° sector.[2]
3. (c)Percentage for 90°.[2]