UPSKILL MATH PLUS

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Let us consider the steps for finding the mean of grouped data using the step deviation method.
 
Steps:
 
1. Calculate the midpoint of the class interval and name it as x_i.
 
2. From the data of x_i, choose any value(preferably in the middle) as the assumed mean(a).
 
3. Determine the deviation (d = x_i - a) for each class.
 
4. Determine the deviation (u = \frac{x_i - a}{h} where h is the class size) for each class.
 
5. Multiply the frequency and u_i of each class interval and name it as f_iu_i.
 
6. Calculate the mean by applying the formula \overline X = a + \left[\frac{\sum fd}{\sum f} \times h \right].
Example:
Find the mean of the following frequency distribution:
 
Class interval30 - 4040 - 5050 - 6060 - 7070 - 80
Frequency1241562001010
 
Solution:
 
Let the assumed mean be a = 55 and class width h = 10.
 
Class interval
Frequency
f_i
Midpoint
x_i
Deviation
d_i = x_i - 55
u_i = \frac{x - a}{h}
f_iu_i
30 - 4012435-20-2-248
40 - 5015645-10-1-156
50 - 6020055000
60 - 70106510110
70 - 80107520220
Total\sum f_i = 500   \sum f_iu_i = -374
We know that the mean of the grouped frequency distribution using the step deviation method can be determined using the formula, \overline X = a + \left[\frac{\sum f_iu_i}{\sum f_i} \times h \right].
Substituting the known values in the above formula, we have:
 
\overline X = 55 + \left[\frac{-374}{500} \times 10 \right]
 
\overline X = 55 - 7.48
 
\overline X = 47.52
 
Therefore, the mean of the given data is 47.52.