Grade 10 Maths · Statistics

Interpret data and draw conclusions

Explain what data shows in real life, for example compare two classes' results or say whether a graph is misleading.

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How to spot a misleading graph - Lea GaslowitzTED-Ed

Impact on median and mean when increasing highest value | 6th grade | Khan AcademyKhan Academy

203 Comparing data with mean, median & rangeMaths Doctor

Types of Sampling Methods (4.1)Simple Learning Pro

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Question b · Siyavula Grade 11 Mathematics, 11.2 Histograms, Worked example 7 · 3 marks

In the previous worked example, the heights of

16

adults were grouped into intervals of length

10 cm

and drawn as the frequency polygon below.
Here is another data set of heights, this time of Grade

11

learners.

132; 132; 156; 147; 162; 168; 152; 174

141; 136; 161; 148; 140; 174; 174; 162

$Diagram for this question$

b Compare the two frequency polygons on one graph to see the differences between the distributions.(3)

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More past paper questions: interpret data and draw conclusions

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3. Question WE8 · Siyavula Grade 10 Mathematics, 10.2 Measures of central tendency, Worked example 8 · 6 marks
WE8 The heights of $10$ learners are measured in centimetres to obtain the following data set:
${150; 172; 153; 156; 146; 157; 157; 143; 168; 157}$
Afterwards, we include one more learner in the group, who is exceptionally tall at $181 cm$ .
Compare the mean and median of the heights of the learners before and after the eleventh learner was included.(6)
Show the memo (6 ticks)Memo
1. ✓
  Mean of 10 learnersmean $= \frac{150 + 172 + 153 + 156 + 146 + 157 + 157 + 143 + 168 + 157}{10} = 155, 9 cm$
  1 mark · Calculate the mean
2. ✓
  Mean of 11 learnersmean $= \frac{150 + 172 + 153 + 156 + 146 + 157 + 157 + 143 + 168 + 157 + 181}{11} = 158, 2 cm$
  1 mark · Calculate the mean
3. ✓
  Median of 10 learnersSorted: ${143; 146; 150; 153; 156; 157; 157; 157; 168; 172}$
  median $= \frac{156 + 157}{2} = 156, 5 cm$
  1 mark · Find the median
4. ✓
  Median of 11 learnersSorted: ${143; 146; 150; 153; 156; 157; 157; 157; 168; 172; 181}$
  median $=$ sixth value $= 157 cm$
  1 mark · Find the median
5. ✓
  Compare the changesThe mean changes by $158, 2 - 155, 9 = 2, 3 cm$ when the outlier (the tall learner) is added, but the median changes by only $157 - 156, 5 = 0, 5 cm$ .
  1 mark · Interpret data and draw conclusions
6. ✓
  ConclusionIn general, the median is less affected by the addition of outliers to a data set than the mean is.
  1 mark · Interpret data and draw conclusions
4. Question a · Siyavula Grade 12 Mathematics, 9.2 Curve fitting, Worked example 4 · 1 mark
Examine the scatter plot below of data collected from a new shop: $Diagram for this question$
a What are the two variables being compared?(1)
Show the memo (1 tick)Memo
1. ✓
  VariablesThe variables being compared are average daily number of customers and time in months.
  1 mark · Interpret data and draw conclusions

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