Grade 11 Statistics: How to Identify the Question Type

Grade 11 Statistics questions work with a single set of data and ask you to summarise it in different ways, a five-number summary, a measure of spread, or a graph. The data and the calculations are often simple; what trips students up is matching the right summary measure or graph to what the question actually asks for.

Type 1: Five-number summary and box-and-whisker plots

Trigger words: "Determine the five-number summary", "Draw a box-and-whisker diagram", "interquartile range"

Trigger structure: A full (ungrouped) data set is given, and you need its minimum, quartiles, and maximum, or a diagram built from those values.

Method (no numbers, just the steps)

Arrange the data in ascending order
Identify the minimum and maximum values
Find the median (Q2): the middle value, or the average of the two middle values
Find Q1 (the median of the lower half) and Q3 (the median of the upper half)
For the interquartile range, calculate Q3 − Q1

Grade 11Paper 2Level 2, Routine Procedures

1.1 Mr Brown conducted a survey on the amount of airtime (in rands) EACH student had on his or her cellphone. He summarised the data in the box and whisker diagram below. [Box-and-whisker diagram over the scale 10 to 66] 1.1.1 Write down the five-number summary of the data. 1.1.2 Determine the interquartile range. 1.1.3 Comment on the skewness of the data.

Source: DBE Mathematics Paper 2, Grade 11, November 2017, Question 1.1

Common mistake

Including the overall median in BOTH the lower and upper halves when finding Q1 and Q3, which skews both quartiles.

See the progression: same type, increasing difficulty

Easy

A data set, in ascending order, is: 4 ; 6 ; 9 ; 11 ; 13 ; 15 ; 18 Determine the median and the interquartile range of the data.

Practice question: not sourced from a past paper.

Medium

A data set, in ascending order, is: 2 ; 5 ; 7 ; 8 ; 10 ; 12 ; 14 ; 17 Determine the five-number summary, and draw a box-and-whisker diagram.

Practice question: not sourced from a past paper.

Hard

A box-and-whisker diagram shows: minimum = 12, Q1 = 20, median = 28, Q3 = 38, maximum = 50. Comment on the skewness of the distribution, with a reason.

Practice question: not sourced from a past paper.

Type 2: Variance and standard deviation

Trigger words: "Calculate the standard deviation", "Calculate the variance"

Trigger structure: A request specifically for how SPREAD OUT the data is around the mean, not just the mean itself.

Do not confuse with: The interquartile range (Type 1), standard deviation uses every value's distance from the MEAN, not just the middle 50% of ordered data.

Method (no numbers, just the steps)

Calculate the mean of the data set
Find the deviation of each value from the mean, and square each deviation
Find the average of those squared deviations, this is the variance
Take the square root of the variance to get the standard deviation

Grade 11Paper 2Level 3, Complex Procedures

1.2 A group of 13 students indicated how long it took (in hours) before their cellphone batteries needed recharging. The information is given in the table: 5 ; 8 ; 10 ; 17 ; 20 ; 29 ; 32 ; 48 ; 50 ; 50 ; 63 ; y ; 107 1.2.1 Calculate the value of y if the mean for this data set is 41. 1.2.2 If y = 94, calculate the standard deviation of the data.

Source: DBE Mathematics Paper 2, Grade 11, November 2017, Question 1.2

Common mistake

Stopping at the variance and reporting it as the standard deviation, forgetting the final square root step.

See the progression: same type, increasing difficulty

Easy

A data set is: 3 ; 5 ; 5 ; 7 Calculate the variance of this data set.

Practice question: not sourced from a past paper.

Medium

Two classes wrote the same test. Class A has a mean of 65% and a standard deviation of 5. Class B has a mean of 65% and a standard deviation of 12. Which class's marks are more consistent? Give a reason.

Practice question: not sourced from a past paper.

Hard

A data set of 5 values has a mean of 10 and a standard deviation of 2. Every value in the data set is then increased by 3. State the new mean and new standard deviation, with reasons.

Practice question: not sourced from a past paper.

Type 3: Ogives (cumulative frequency curves) and grouped data

Trigger words: "Draw an ogive", "Use the ogive to estimate...", data given in class intervals

Trigger structure: Data is given in grouped intervals (e.g. '10 ≤ x < 20') rather than as individual values, often building up to a cumulative frequency graph.

Do not confuse with: The five-number summary from raw data (Type 1), with grouped data you read estimates off a cumulative frequency graph instead of calculating exact quartiles from individual values.

Method (no numbers, just the steps)

Calculate the cumulative frequency by running total down the frequency column
Plot each cumulative frequency against the UPPER boundary of its class interval
Join the points with a smooth curve to form the ogive
To estimate a quartile or median, draw a horizontal line from the relevant cumulative frequency value to the curve, then drop down to read off the estimated data value

Grade 11Paper 2Level 3, Complex Procedures

2 A student conducted a survey among friends and relatives to determine the relationship between age and the number of marketing phone calls received in a month: 20 < x ≤ 30: frequency 7 30 < x ≤ 40: cumulative frequency 27 40 < x ≤ 50: frequency 25 50 < x ≤ 60: cumulative frequency 64 60 < x ≤ 70: cumulative frequency 72 70 < x ≤ 80: frequency 4 80 < x ≤ 90: cumulative frequency 80 2.1 Complete the frequency and cumulative frequency columns. 2.4 Draw an ogive to represent the data. 2.5 Determine the percentage of marketing phone calls received by people older than 54 years.

Source: DBE Mathematics Paper 2, Grade 11, November 2017, Question 2

Common mistake

Plotting cumulative frequency against the midpoint of each interval instead of its upper boundary.

See the progression: same type, increasing difficulty

Easy

A frequency table shows: 0–10: 5 learners, 10–20: 8 learners, 20–30: 12 learners, 30–40: 5 learners. Determine the cumulative frequency for each interval.

Practice question: not sourced from a past paper.

Medium

An ogive for 50 learners' test scores passes through the point (45 ; 38), meaning a score of 45 corresponds to a cumulative frequency of 38. Estimate how many learners scored MORE than 45.

Practice question: not sourced from a past paper.

Hard

An ogive for 80 data values is used to estimate Q1 = 22, median = 35, and Q3 = 50. Estimate the interquartile range, and use it to determine whether a value of 75 would be considered an outlier (an outlier is more than 1,5 × IQR above Q3).

Practice question: not sourced from a past paper.

Words like determine and hence appear throughout this topic, see the instruction word glossary for full definitions.