Question

Find the mean using all three methods

Answer 1

☯ Following data  $\\ \begin{gathered}\\ \begin{gathered}\boxed{\begin{array}{c|c|c|c|c|c}\bf Class\: interval&\sf 25 - 30&\sf 30 - 35&\sf35 - 40 &\sf 45 - 50&\sf 50 - 55\\\frac{\qquad \quad \qquad}{}&\frac{\quad \qquad \qquad}{}&\frac{\qquad \quad\qquad}{}&\frac{\qquad \quad \qquad}{}&\frac{\quad \qquad \qquad}{}&\frac{\qquad \quad\qquad}{}\\\bf Frequency&\sf 25&\sf 34&\sf 50&\sf 42&\sf 38\end{array}}\end{gathered} \\\end{gathered}$━━━━━━━━━━━━━━━━━━━━

There are three methods for finding the mean from a grouped frequency table.

• There are three methods for finding the mean from a grouped frequency table.Method 1: Direct method.
• There are three methods for finding the mean from a grouped frequency table.Method 1: Direct method.Method 2: Assumed Mean method.
• There are three methods for finding the mean from a grouped frequency table.Method 1: Direct method.Method 2: Assumed Mean method.Method 3: Step Deviation method.

Arithmetic Mean by Direct Method - formula

∑i=1nf= Sum of all the frequencies. This is also denoted by N. ∑i=1nfixi= Sum of the product of frequencies and corresponding observations.

In statistics, the assumed mean method is used to calculate mean or arithmetic mean of a grouped data. ... This method depends on estimating the mean and rounding to an easy value to calculate with. Again this value is subtracted from all the sample values.

Step Deviation mean Method: The first step is to choose one among the xi's as the assumed mean, and denote it by 'a'. Second step is to find ui = $(x_i - a)/h$, where a is the assumed mean and h is the class size.

Answer 2

Answer:

☯ Following data

Frequency

25−30

25

30−35

34

35−40

50

45−50

42

50−55

38

━━━━━━━━━━━━━━━━━━━━

There are three methods for finding the mean from a grouped frequency table.

There are three methods for finding the mean from a grouped frequency table.Method 1: Direct method.

There are three methods for finding the mean from a grouped frequency table.Method 1: Direct method.Method 2: Assumed Mean method.

There are three methods for finding the mean from a grouped frequency table.Method 1: Direct method.Method 2: Assumed Mean method.Method 3: Step Deviation method.

Arithmetic Mean by Direct Method - formula

∑i=1nf= Sum of all the frequencies. This is also denoted by N. ∑i=1nfixi= Sum of the product of frequencies and corresponding observations.

In statistics, the assumed mean method is used to calculate mean or arithmetic mean of a grouped data. ... This method depends on estimating the mean and rounding to an easy value to calculate with. Again this value is subtracted from all the sample values.

Step Deviation mean Method: The first step is to choose one among the xi's as the assumed mean, and denote it by 'a'. Second step is to find ui = (x_i - a)/h(x

i

−a)/h , where a is the assumed mean and h is the class size.