MEASURES OF DISPERSION FOR UNGROUPED DATA

Which set of data has the largest range?

• 30, 24, 40, 25, 22, 34

• 23, 20, 44, 26, 45, 39

• 36,49,55,38,58,42

• 64, 48, 50, 46, 44, 62

The table shows the achievement of four classes in a Mathematics test.

Which class shows the most consistent achievement in the test?

• 4M

• 4N

• 4P

• 4S

The stem-and-leaf plot shows the masses, in kg, of two groups of pupils.

Find interquartile range of the masses for each group of pupils.

• P: 14 kg; Q: 31 kg

• P: 31 kg; Q: 14 kg

• P: 42 kg; Q: 38 kg

• P: 56 kg; Q: 64 kg

The frequency table shows the scores obtained by a group of pupils in a competition.

If the interquartile range is 3, state one possible value of x.

• 1

• 2

• 5

• 6

Based on the information of a set of data in the above table, which box plot represents the set of data correctly?

• 
• 
• 
• 

The mean of a set of numbers p, 2p, 3p, 4p and 5p is 6. Calculate the standard deviation of the set of numbers.

• 2.288

• 2.828

• 8.228

• 8.822

Based on the box plot, determine the range and interquartile range.

• Range: 2.1; Interquartile range: 4.2

• Range: 2.2; Interquartile range: 4.4

• Range: 4.2; Interquartile range: 2.1

• Range: 4.4; Interquartile range: 2.2

The range and the variance of a set of numbers y1, y2, ... , y15 are 8 and 4.5 respectively.

Calculate the range and the variance of the set of numbers $\frac{2y_1+15}{5},\ \frac{2y_2+1}{5},\ \frac{2y_3+1}{5},\ ...\ ,\ \frac{2y_{15}+1}{5}.$ 

• 3.4, 3.2

• 3.4, 2

• 3.2, 3.6

• 3.2, 3.8

A set of data contains 20 numbers. The sum of the numbers is 284 and the sum of the squares

of the numbers is 4 688.

Calculate the standard deviation of the set of data.

• 5.274

• 5.724

• 32.76

• 36.27

The variance of a set of positive numbers p, (p - 5), (p - 2),

(p - 3) and (2p - 5) is 5.84.

Calculate the value of p.

• 5

• 6

• 7

• 8