Maths Maestri
Grade 11 Mathematics · Statistics: Ungrouped Data
Topic: Statistics: Ungrouped Data  ·  Grade: 11
Questions: 16  ·  Skills: Central tendency · Dispersion · Quartiles · Five-number summary · Box-and-whisker · Standard deviation · Skewness & outliers

What this quiz covers

Grade 11 Ungrouped Data Quiz 1 draws its questions at random from 16 questions across these topics:

Worked examples

A few of the question types, with full solutions, so you know what to expect.

Central Tendency. Calculate the mean of the data set: 12, 8, 15, 5, 10.

  1. 10
  2. 9
  3. 11
  4. 50

Answer: 10

Add every value: \( 12 + 8 + 15 + 5 + 10 = 50 \).

Divide by the number of values \( (n = 5) \): \( \bar{x} = \dfrac{50}{5} \).

The mean is the "average" - the sum of the values over how many there are.

Central Tendency. Find the median of: 3, 9, 4, 7, 6.

  1. 5
  2. 6
  3. 7
  4. 4

Answer: 6

First put the data in order: 3, 4, 6, 7, 9.

There are \( n = 5 \) values (odd), so the median is the middle (3rd) value.

Central Tendency. Find the median of: 10, 4, 8, 6, 12, 2.

  1. 8
  2. 7
  3. 6
  4. 6,5

Answer: 7

Order the data: 2, 4, 6, 8, 10, 12.

There are \( n = 6 \) values (even), so average the two middle values (3rd and 4th):

\( \text{median} = \dfrac{6 + 8}{2} = \dfrac{14}{2} \)

Central Tendency. What is the mode of: 4, 7, 4, 9, 4, 7, 2?

  1. 7
  2. 4
  3. 2
  4. 9

Answer: 4

The mode is the value that appears most often.

Count them: 4 appears three times, 7 appears twice, and 2 and 9 once each.

Dispersion - Range. Calculate the range of: 23, 11, 45, 30, 18.

  1. 45
  2. 34
  3. 22
  4. 27

Answer: 34

Range = maximum value - minimum value.

Maximum \( = 45 \), minimum \( = 11 \).

\( \text{Range} = 45 - 11 \)