The capacities of ten engines, in litres, are given rounded to 2 decimal places, as follows: 

$1.86,2.07,1.74,1.08,1.99,1.96,1.83,1.45,1.28$ and $2.19$.  

These capacities are to be grouped in three classes as $1.0-1.4,1.5-2.0$ and $2.1-2.2$

.Find the frequency of the class $1.5-2.0$ litres.

The capacities of ten engines, in litres, are given rounded to 2 decimal places, as follows: $1.86,2.07,1.74,1.08,1.99,1.96,1.83,1.45,1.28$ and $2.19$.

These capacities are to be grouped in three classes as $1.0-1.4,1.5-2.0$ and $2.1-2.2$

Find the frequency of the class $1.5-2.0$ litres.

Write down two words that describe the type of data given about the engines.

Over a $10$-day period, Alina recorded the number of text messages she received each day. The following stem-and-leaf diagram shows her results.

$$\begin{gathered} \begin{array}{lllllll}\mathbf{0}& 9& & & & & \\ \mathbf{1}& 0& 3& 4& 4& & \\ \mathbf{1}& 5& 5& 5& 6 8& & \end{array} \\ \mathrm{Key}: \mathbf{1}\mid 5 \\ \mathrm{represents} 15 \mathrm{messages} \end{gathered}$$

On how many days did she receive more than $10$ but not more than $15$ messages?

Over a $10$-day period, Alina recorded the number of text messages she received each day. The following stem-and-leaf diagram shows her results.

$$\begin{gathered} \begin{array}{lllllll}\mathbf{0}& 9& & & & & \\ \mathbf{1}& 0& 3& 4& 4& & \\ \mathbf{1}& 5& 5& 5& 6 8& & \end{array} \\ \mathrm{Key}: \mathbf{1}\mid 5 \\ \mathrm{represents} 15 \mathrm{messages} \end{gathered}$$

How many more rows would need to be added to the stem-and-leaf diagram if Alina included data for two extra days on which she received $4$ and $36$ messages? Explain your answer.

The following stem-and-leaf diagram shows eight randomly selected numbers between $2$ and $4$ .  

$$\begin{gathered} \begin{array}{ll}2& 1 3 3 a \\ 3& b 5 6 7 \end{array} \\ \mathrm{Key}: 2\mid 1 \mathrm{represents} 2.1 \end{gathered}$$

Given that $a-b=7$ and that the sum of the eight numbers correct to the nearest integer is $24$, find the value of $a$ and $b$.

Eighty people downloaded a particular application and recorded the time taken for the download to complete. The times are given in the following table.

Find the number of downloads that completed in $5$ to $6$ minutes.

Eighty people downloaded a particular application and recorded the time taken for the download to complete. The times are given in the following table.

Find the number of downloads that completed in $5$ to $6$ minutes.

On a histogram, the download times from $5$ to $6$ minutes are represented by a column of height $9.6 \mathrm{cm}$. Find the height of the column that represents the download times of $6$ to $10$minutes.

A histogram is drawn with three columns whose widths are in the ratio $1: 2: 4$. The frequency densities of these classes are in the ratio $16: 12: 3$, respectively.

Given that the total frequency of the data is $390$ , find the frequency of each class.

A histogram is drawn with three columns whose widths are in the ratio $1: 2: 4$. The frequency densities of these classes are in the ratio $16: 12: 3$, respectively.

Given that the total frequency of the data is $390$ , find the frequency of each class.